There Is Little Pressure To Improve Contract Drafting
One piece of the puzzle is tradition and habitual writing style. A customary writing style for legal documents evolved over time, some of those conventions have evolved overtime (e.g. "Party of the first part, party of the second part"), others have not.
Archaic vocabulary is slowly being weeded out, but again, it is almost never the goal of someone drafting a contract to reduce the reading level of the document. As long as the judge, or other lawyers, know what it means, it is an aesthetic stylistic issue more than it is a substantive issue of importance.
Contract drafting is highly decentralized and change happens only when there is a powerful impetus for change.
Does this mean that legal writing can't be improved?
Some lawyers are excellent writers in both contract drafting and in court documents.
A well drafted contact can reduce litigation costs when there are disputes. It can also increase compliance with the intent of the parties by preventing disputes over what the contract means from arising in the first place.
But most lawyers are mediocre contract drafters, and there is little selective pressure in transactional legal work to weed out their sub-optimal writing styles.
Bryan A. Garner, who among other things is the editor of Black's Law Dictionary, is pretty much the leading figure in the United States pushing for a more modern, more readable, less flabby legal writing style. This is exemplified, for example, in his book "Legal Writing in Plain English" (2d ed. 2013).
But even then, a lot of the impetus for his stylistic decisions was primarily driven by the need to get across ideas clearly, in a minimum of words, when writing appellate briefs with word limits. This is also the main context in which legal writing is taught in law school and continuing education classes.
In contracts, in contrast, in our current era of the word processor, long documents are easy to deliver, and long passages of writing can be cut and pasted. So, the same outside pressures to limit word counts and persuade judges who will read legal briefs cover to cover in order, are not present when drafting contracts. So, the pressure to have a succinct plain language writing style in contracts is less strong.
This said, when there has been regulatory pressure to write consumer contracts in a way that an average consumer can understand, it can be done.
For example, most credit card agreements are written in very clear plain English with a very low reading level compared to other contracts.
But those easy to read credit card agreements are drafted by committees of many lawyers and senior executives, each charging hundreds of dollars an hour, over many meetings over a period of weeks of debate and refinement, and a cost of many tens of thousands of dollars each to draft.
The flabby and clunky character of legal writing also reflects client imposed budgetary constraints. It takes much more time and effort, with multiple rounds of rewriting and editing, to write a clean, easy to read contract than it does to write a kludgy one.
Lawyers bill by the hour and clients want the job done at a price that they can afford. There is little incentive in contracts that will not be used many times as forms, to take the effort to produce a clean, easy to read final product. This kind of beautifully drafted contract costs much more to draft for the client, but provides little additional legal benefit to the client.
Few contracts are ever litigated at all, and when they are, the legal drafting tends to focus on only a handful of key provisions that are carefully drafted. Boilerplate language, which is often less carefully drafted, is very rarely litigated, so the quality of that writing doesn't matter much.
As far as capitalization goes, I agree with @user6726 that all caps writing is often required by law. These requirements were based upon the previous legislative assumption that it was more prominent and more likely to be read, which has since been proved to be false empirically. But new empirical discoveries about readability haven't changed the relevant laws requiring certain language in contracts to be "prominent" and in all caps.
I would also add that there is a legal writing convention that defined terms have capital letters (although not necessarily all caps), which is a pointer to when one needs to look for a definition, that relaxes the need to put the definitions of capitalized words in the actual sentence where those terms are used.
Weird capitalization can facilitate shorter sentences.
The Relevant Audience
I'd also agree that the primary audience for contract language is often not an unsophisticated non-lawyer consumer. While it's true that the average American reads at about the 5th grade level and can't do algebra, that person isn't the target audience. In the same vein, you don't write scientific journal articles for an audience of the average American.
When push comes to shove, written contracts are interpreted as a matter of law by judges who are legally trained, and not a matter left to a jury of non-lawyers to decide.
Most business to business contracts are negotiated by lawyers. Most business to business contracts have as additional audiences sophisticated senior managers of business with some limited formal business law training in college, who also have great familiarity with the class of contracts involved.
Even in consumer contracts, when consumer protection regulations and statutes do not compel another approach, the intent is frequently a MEGO effect (My Eyes Glaze Over) in the hope that the consumer, who often isn't at liberty to negotiate the terms anyway, won't decide to read the fine print.
The only language in a contract that needs to be clear to the consumer is the actionable part like the price that needs to be understood by the consumer to perform it. And, often those parts of a contract are provided in a separate short summary document with the full contract available for future reference but not intended to be routinely read in full.
Furthermore, characteristic legal writing styles can convey a sense of importance and official authority. It sounds like it is and is intended to have legal effect. It's the same reason that fictional magical spells are far more often in Latin or Greek or Sumerian than they are in plain English. Language too ordinary conveys the false impression to a client that anyone could write the contract even if legal skill is implicated in drafting it, and can even cast doubt over whether a document was intended to be a legally binding contract in the eyes of a non-lawyer encountering it.
Long Sentences, Definitional Clauses, And Pronouns
One of the key factors that is identified as making legal writing hard to read is the use of internal definitional clauses within sentences and the use of very long sentences.
It is possible to draft without those. But, often including it in the same sentence reflects the drafting lawyer's thought process.
It can also reflect a negotiated contract drafting process. Even if an initial draft of a contract has simple sentences clearly laid out, it may be easiest to clarify a bargaining point in contracting negotiations by complicating the sentence in question to make it reflect the other side's preferred interpretation, even if it is stylistically ugly. And, changing that language in a final draft to make the contract look pretty is viewed with the suspicion that a subtle substantive change in the meaning of the contract from the haggled term was intended.
As an aside, some contract provisions in hotly negotiated contracts are also sometimes intentionally ambiguous. This is because resolving the ambiguity could result in a fight over a side issue that could bust the deal if each side insisted on their own interpretation. Leaving the term ambiguous allows a judge evaluating a dispute that actually arises, if a dispute even arises over that term (which it often doesn't), in order to do what makes sense under the circumstances instead.
Also, lawyers are wretchedly afraid of an adverse party quoting a sentence in a contract without including the related context that clarifies its meaning (e.g. by omitting definitions that are not obvious from the plain language of the contract).
Unlike most prose, contracts are rarely read front to back the way you would a court opinion or a newspaper report or a short story. Normally, someone using a contract quotes only the relevant portion of the contract in isolation from the larger entire document.
When ideas are broken into separate sentences, lawyers are very worried, rightly or wrongly, that different sentences in a paragraph or section modify each other, rather than being isolated islands of legal propositions. So lawyers are more comfortable when as many connected ideas as possible are all contained in the same sentence in which everything must be related somehow.
Lawyers feel more comfortable and secure arguing about the meaning of a single sentence, than they do arguing that a simple short sentence should have a particular meaning based upon the larger context in which it is found.
Similarly, lawyers are quite wary about using pronouns that aren't defined terms in the contract, for fear that the person that the pronoun refers to will be incorrectly assigned, even though this is an unnatural way of writing.
Common Law Contracts v. Civil Law Contracts
Also, as an aside, contract drafting is an area where common law legal drafting styles differ materially from civil law country legal drafting styles (e.g. in continental Europe).
This is because in civil law countries there is a great effort made to provide for what would usually be boilerplate language in U.S. contracts as default statutory rules that match the default choices that are usually made in contracts negotiated between third-parties. Far less can be taken for granted in common law countries.
A lot of the operative language in a common law jurisdiction contract, including much of it the most difficult to read legalese in contracts, is simply implied in law unless specifically disavowed, in many civil law countries.
As a result, civil law country contracts are usually much shorter and more focused on the deal specific terms than a common law jurisdiction contract. A civil law business agreement that runs to five pages might typically take 30-40 pages to write saying exactly the same thing in a common law jurisdiction.