In theory "legalese" is English: you will find every word in the dictionary, and the rules of grammar are exactly the same.
However in practice it is true that legal documents are often written in a very specific style. There are a number of possible reasons for this:
The document must say what it intends very precisely. Most regular language is quite sloppy and ambiguous, but lawyers share with computer programmers the need to ensure that what is said is precisely what is meant.
A legal document exists within a legal system in which certain words or phrases carry very specific meanings. For instance in the UK the words "in trust" when talking about money or property will automatically import a huge body of law (and its also possible to have that law apply even if you don't use the magic words). Lawyers know about these things, and will write a document to either invoke or avoid those bodies of law as they see fit.
Related to (2) above, laws and legal precedents give lists of things that must be done or proved. Legal documents will often follow these lists using the same terms in order to avoid future challenges. For instance US patent law specifies what must go into a patent application, so you had better follow the format and use the same subject headings.
Within patents in particular, the patent office manual allows a patent to be rejected because of informal language that leaves the patent unclear. Patent lawyers and examiners have evolved an informal set of conventions about how things are said. If you use these conventions the examiner will have a much easier time understanding what you mean. Its not "cargo cult", more a specialised language.
(Note: the following is about the US patent system, but similar considerations apply everywhere.)
Lets take a look at an example patent picked at random:
The abstract lists the key elements of the invention in very abstract terms, such as "vibrating mechanism" and "power source". If you were writing this in "informal" language you might mention a specific power source such as a battery. But doing so limits your invention: what if something other than a battery (such as a super-capacitor or spring-driven generator) is used? That would be a separate invention not covered by your patent. So patent lawyers take time to think and ask about generalisations.
The next interesting part is the Claims. These set out precisely what is and is not covered by the invention. If the Claims don't cover it then its not in the patent. The format of each Claim is defined in 35 US 112, so if you don't do it like that it won't count.
Finally we get to the Description. This is intended to explain the invention to "any person skilled in the art". It also needs to explain the prior art and show why the invention is new and useful, because those are statutory requirements. Much of this is in fact written in an ELI5 way, if the 5-year-old had swallowed a dictionary. The reason is that any little thing omitted or assumed can be used by a future challenger claiming that the hypothetical "person skilled in the art" would have failed to understand or know it.
So lets take a sample paragraph from this patent (numbers refer to diagrams in the patent):
The electrical connection 22 may include a circuit device that transforms a DC power provided by the power source 26 to AC power for the vibrating mechanism 28, which circuit devices are known to those having ordinary skill in the art of circuit design.
This anticipates a possible variation on the invention and stops it being patented separately. It asserts that the "circuit devices" are known, so it doesn't need to describe them in detail. If that assertion wasn't there then someone might challenge the patent on that point, but since the assertion has been accepted by the patent examiner it is presumed to be correct. Note the "... ordinary skill in the art ..." phrase: this is explicitly calling out to the language in Title 35.
You might imagine that such a variation would be obvious, and therefore not patentable. However it is very difficult for a court to decide in hindsight whether something would really be obvious to a person skilled in the art; you wind up with each side hiring expert witnesses who will give competing testimony as to whether it seems obvious to them. As a result the courts have set a very low bar to a claim that something is "non-obvious".
The language used throughout a patent is of vital importance: infringement cases can hinge on the most trivial of linguistic issues. This blog post by a patent lawyer has a list of examples, including this one:
For example, in Chef America, Inc. v. Lamb-Weston, Inc., Chef America tried to protect a cooking step for heating a dough at a certain temperature inside an oven. But Chef America drafted the claim to read “heating the . . . dough to a temperature in the range of about 400 degrees F. to 850 degrees F.” The Federal Circuit reasoned that “to” is not “at” and, thus, the claim required the dough (not the oven) to be heated to the specified temperature. The Court then ruled that the claim was not infringed. In fact, under the Court’s claim construction, this claim could not possibly be infringed unless one wanted to make burned dough.
See also this case on "partially" not including "totally", and this post on why the word "disclosure" is now used instead of "invention". Patent lawyers call this kind of thing "patent profanity", i.e things you simply do not say.
So if you don't use this kind of "legalese" in your patent the following things are much more likely:
Your application will be rejected because the examiner cannot understand exactly what your invention consists of.
Trivial variations on your invention will turn out not to be covered.
Someone will challenge your patent on the grounds that you didn't explain everything that a "person skilled in the art" might need to know.