Answering separately:

...I'd call it a failed US-wide attempt to standardize...

The LOC Classification is a system for organising a printed (and largely bound) corpus on physical shelves/stacks. That is, any given document can occupy at most one and only one location, and two or more documents cannot occupy the same location, if they comprise separate bound volumes or other similar formats (audio recordings, video recordings, maps, microfilm/microfiche, etc.).

For digital records, this constraint isn't as significant (your filesystem devs will want to ensure against multiple nonduplicate records having the same physical address, but database references and indices are less constrained).

The Subject Headings provide ways of describing works in standardised ways. Think of it as strongly similar to a tagging system, but with far more thought and history behind it. ("Folksonomy" is a term often applied to tagging systems, with some parts both of appreciation and frustration.)

Where a given work has one and only one call number fitting within the LoC classification, using additional standardised classifications such as Cutter Codes, author and publication date, etc., works typically have multiple Subject Headings. Originally the SH's were used to create cross-references in physical card catalogues. Now they provide look-up affordances in computerised catalogues (e.g., WorldCat, or independently-derived catalogues at universities or the Library of Congress itself). You'll typically find a list of LoC SH's on the copyright page of a book along with the LoC call number.

Back to the Classification: there are many criticisms raised about LoC's effort, or others (e.g., Dewey Decimal, which incidentally is not free and is subject to copyright and possibly other IP, with some amusing case history). What critics often ignore is that classifications specifically address problems of item storage and retrieval, and as such, are governed by what is within the collection, who seeks to use that material, and how. In the case of state legal classifications, absent further experience with both that section of the classification (section K of the LoC Classification) and works within it, I strongly suspect that the complexity variation is a reflection of the underlying differences in state law (as noted above) and those wishing to reference it. That is, NY, CA, and PA probably have far greater complexity and far more demanding researchers, necessitating a corresponding complexity of their subsections of that classification, than do, say, Wyoming, North Dakota, and South Dakota (among the three smallest sections of state law by my rather faltering recollection).

Peculiarities of both the Dewey and LoC classifications, particularly in such areas as history (LoC allocates two alphabetic letters, E and F respectively, to "History of the Americas), geography, religion, etc. In the case of Dewey, Religion (200) is divided into General Religion (200--209), Philosophy and Theory of Religion (210--219), then the 220s, 230s, 240s, 250s, 260s, 270s, and 280s to various aspects of Christianity. All other religions get stuffed into the 290s. Cringe.

Going through LoC's Geography and History sections one finds some interesting discontinuities particularly following 1914--1917, 1920, 1939--1945, and 1990. There are of course earlier discontinuities, but the Classification's general outline was specified in the early 1800s, and largely settled by the late 1800s / early 20th century. Both the Classification and Subject Headings note many revisions and deprecated / superseding terms. Some of that might attract the attention of the present Administration, come to think of it, which would be particularly unfortunate.

The fact that the LoC's Classification and SH both have evident and reasonably-well-functioning revision and expansion processes and procedures actually seems to me a major strength of both systems. It's not an absolute argument for their adoption, but it's one which suggests strong consideration, in addition to the extant wide usage, enormous corpus catalogued, and supporting infrastructure.