My daughter did take the SAT, but we moved areas and the high school in the new area, as it turned out, didn't bother to get any of the test results from the kids who moved in. They just put them automatically into the bottom set for maths and science, the two subjects they streamed. (fyi She got maximum score for maths, near maximum in science .)
My daughter's primary school was way ahead in maths, so despite being only taught simple stuff she had learned years before during year 7, she was consistently getting test results the same as the top end of the top stream. They did grudgingly offer her the chance to move (in an offputting way designed to discourage her luckily she took up the offer anyways). However she seemed to be the only child in year seven who changed streams.
In science, we were more dependent on what the high school was actually teaching. The kids in the bottom set receive the same tests, but are taught a lot less material so are fundamentally disadvantaged; the idea that "they can easily move up" is not something I recognise. During the year her test scores were well above the rest of her class, but below the middle class because of specific topics not covered by her class. She finished year seven at the same level as year six (5a), making the year look like a waste of time. This year (year 8) she was moved up to the middle class, and then was achieving test scores equal to the top scores in the top class. It still took most of the year till she was moved up to the top class. Meanwhile, her interest in science has really taken a tumble.
Of course, it depends very much on the specific high school, but I would say there is definitely a risk if they are not taken (and, obviously a risk if they are taken and ignored!), And I would be sceptical about schools' claims that they take great care in allocating people to the right streams our high school made plenty of claims about that!
And being put in inappropriately easy classes is not great for the kids. My daughter was bored stiff in the lower classes, but really interested once working at a suitable level and pace.