"It's pretty obvious you don't understand how pervasive the test material stuff has "infected" everyday teaching in many states.
You're talking about a different phenomenon of actual cheating on tests where teachers give students answers (or something close to it). That's not the kind of preparation that goes on in most classrooms."
Actually, I do, and that is exactly the 'prep' that is going. My father taught 5th grade for 30 years and I watched and listened how things changed over the years - and his complaints that his kids still did better than the teachers that broke open the packages and copied the tests, but the admins didn't give a shit. As a college instructor, I'm well aware that the kids haven't even learned to follow the most basic directions like where to put their name on their paper. With respect to you, most of the high-school and elementary students have been failing in their job because they'd rather be the 'cool' teacher than the 'tough' teacher. While part of that is because the ability to discipline was stripped from them, it's not all.
"In many states, the standardized tests are derived from state-approved "standards" that spell out specific exercise types which are likely to occur (particularly in basic subjects like math and reading). Teachers who have any experience with these tests over the years notice certain patterns of the types of questions that always show up. (This isn't just for normal "standardized testing" -- it goes for AP tests and such as well. When I taught AP physics, there were all sorts of "lore" passed down among AP teachers because all the previous tests were available, so you knew there was likely to be a question dealing with X, a question on topic Y would probably take a certain form, etc.)"
This is actually nothing new. There was always 'lore' about what was going to be on the test, why do you think the old question "A car is going 90 miles an hour one way..." was basically a meme from the 50s/60s/70s/80s? There were always, and are always going to be specific types of questions because those are relevant constructions of relevant knowledge. The point was always to SHOW YOUR WORK. (In a multiple choice, the answers to choose from were always so close that you needed to be right, not fudging, to get the question correct).
"For example, a disproportionate number (95%+) of math problems involving right triangles would involve either (1) the Pythagorean triple 3,4,5 or its multiples, or (2) the triple 5,12,13. (It's possible that 8,15,17 could show up too maybe... but I think it was just the first two which were common.)"
You seem to think that this is somehow new. The GRE and SAT doesn't go much farther (if at all) than this either. They're just testing to see if you know the theory and can apply it at it's basic level. Perhaps a math instructor's opinion of 'deep knowledge' is a bit more expecting.
Beyond math, reading comprehension is reading comprehension. You can't really 'boost' it without practicing, so that's again a moot issue.
There are issues with some of these new ways to do old problems - reinventing the wheel is always a stupid undertaking - but otherwise most of the problem is new teachers thinking the old ways need changing because of problematic social outcomes. It was never the ways of teaching, it was the teachers (and admin)