Let me make a comparison.

If your manager says your performance is based on lines of code, you will be incentivized to write lots and lots of code. Does lots and lots of code mean you are being productive and making good software? Sometimes yes! Sometimes heaps of code means you are being ultraproductive and making amazing software. It could also mean you are writing much more code than you need to, introducing new bugs, not thinking about generalizing patterns, creating technical debt, making a worse UX, all of which I'm guessing you would agree are important to software engineering. But none of those things are going to matter in the lines of code metric.

So yes, sometimes having metrics for performance are worse than imperfect. Sometimes they are antithetical to the supposed goals. Student time is a zero sum game, and having a large portion of a crucial time in their development spent cramming for one metric is not going to have good outcomes for a society, only good outcomes for a metric.

SAT prep per se is an unbelievably shitty thing for people to waste their time on. It's largely mindless and uninteresting, stifles rather than encourages curiosity, emphasizes judging people by substantially arbitrary numerical scores, gives the false impression that some people are inherently better than others, and, in the medium to long term, is a grossly inefficient way to improve performance on the SAT.

If you want your own kids to get a high SAT language score when they are high school students, the top things you can do to help them are: (1) read aloud to them when they are very young, as much as you have time for, ideally choosing excellent books of wide variety, (2) keep reading aloud to them when they are older, (3) encourage them to read for pleasure, (4) converse about the world with them, without condescending.

If you want your own kids to get a high math score, (1) surround them with technical materials (construction toys, logic puzzles, board games, circuit parts, programmable robots, or whatever) and play with them together – or if on a tight budget, improvise materials from whatever you have at hand, and (2) spend time working non-trivial word problems one-on-one. Start from https://archive.org/details/creativeproblems0000lenc

If you have the personal time to do these steps, you won't have to give a shit about what their SAT score is, because it will be good enough for whatever they need it for. (Sadly as a society we don't have the resources or motivation to get every child enough listening-to-books-read-aloud time or enough playing-with-technical-materials-with-adult-help time, so we try to replace it with cheaper and more scalable vacuous alternatives like multiplication drills, spelling quizzes, and SAT prep.)