The US Constitution now has 27 amendments. I noticed that these amendments are "attachments" to the original US Constitution. Why don't the constitutional amendments directly modify the text of the original US Constitution? This seems to be different from how other laws are modified, where bills propose to modify the text of existing laws. Is there a legal or historical reason for this?
The best explanation is "tradition", followed by "Congress does not actually rewrite laws" (it passes laws whose effect changes what counts as the law). Traditionally, Congress would enact some law, then it could later enact a law which effectively modifies existing laws. That modification could be implicit, by stating a new legal fact, which "corrects" some earlier legal fact. For instance, the 6th Congress enacted a law (session I, p. 4: Ch. III in second volume) entitled "An Act supplementary to the act, intituled 'An Act to provide for the valuation of Lands and Dwelling Houses, and the enumeration of slaves, within the United States'", which was enacted by the 5th Congress Ch. LXIX, p. 580. The amendment added a power to the commissioners created by the first act "to revise, adjust and vary valuations". This is done by simply stating a new power, and does not require re-writing the entire earlier text – it was understood that the new act "overrides" the old act.
Contemporary statutory practice (as opposed to constitutional practice) is that congressional acts which revise older laws will state, in some fashion, how the previous law should be edited. Officially speaking, the law "is" the historical sequence of acts of Congress and therefore Congress does not actually rewrite laws (except on some occasions where it does).
An example of an editing instruction enacted by Congress is an amendment to the Immigration and Nationality Act which states that
(n) IMMIGRATION AND NATIONALITY ACT.— (1) Section 411(b) of the Immigration and Nationality Act (8 U.S.C. 1521(b)) is amended by striking "and under the general policy guidance of the United States Coordinator for Refugee Affairs (hereinafter in this chapter referred to as the 'Coordinator')" and inserting "the Secretary of State".
It is very difficult to keep track of the hundred of thousands of acts of Congress making up the Statutes at Large, therefore we also have the US Code system which effectuates the various historical changes. For the most part, the codified (re-written) laws accurately reflect the complex sequence of statutes passed by Congress. though there was a whoops-moment when The Act of Sept. 7, 1916, 39 Stat. 753 §92 was omitted from inclusion of the US Code because it was mistakenly thought that that section had been repealed (sorted out in 1993).
Given how few and how autonomous the amendments to the US Constitution have been, there is no compelling need to adopt a "wholesale rewrite" model of amendments for the Constitution, though the election of POTUS is one area where it might make sense to delete previous text (still, it's not difficult to read the whole document, as opposed to reading the entirety of the Statutes at Large).
A wholesale rewriting of the US Constitution is possible, and happened in 1787. This is still a possibility, but not one which gains sufficient popular support. Until there is a sufficiently large call for an actual rewriting of the US Constitution, we will followed this particular method of amending the Constitution.