What could explain why a high school in a rich city has a far higher rate of students with learning-disabled designations than the national average?

Details that Newton has a higher percentage of kids with phony learning disabilities than Boston?
No I have no details,just a hunch.

I've observed BPS's testing for initial IEPs for incoming three-year-olds, and have seen instances in which the person testing did not meet the qualification level of the test author and was not administering it remotely correctly. I've had them administer testing in which a student came out as extremely gifted, when having come out in the mildly delayed range when tested by every other qualified clinician who has seen the child. I've been told by employees there that they're encouraged to find students ineligible for 3yo placements, because it costs money. For kids who are past compulsory age, it brings in money, so different ballgame. I've also been in meetings where all of the outside folks are recommending a type of setting that BPS doesn't have (this often comes up with kids of normal intelligence who need a small, quiet classroom and/or classroom using a specific approach while the BPS boilerplate policy is that most kids with normal intelligence and no major disruptive behavior go into regular ed or integrated), and the BPS team is stating it's off the table because they don't have it, without any clinical justification for why they won't be providing it. This is very much illegal, but not so drastically that DOE will do anything, and BPS knows most families won't sue them for something that would require a private lawyer.

BPS doesn't provide services based on outside testing or on diagnoses, which they're not required by law to do. Many local districts DO provide services based on outside testing or on diagnosis, which is what they choose to do and which is permitted. This then leads to clinicians telling families that of course a child with a particular diagnosis will get a 3yo classroom placement, and then when they don't, the family has nothing in place as a backup, or worse, the clinician just decides the family didn't actually go through the process, and reports them for educational neglect (which it's not, provided the parent is doing functional things with them at home, but there's also a misconception among providers that it's the law that 3yos with a disability have to be in school).

And quit. Remember when they were told they had to let gay parents adopt from their orphanages? They took their ball and went home instead.

Of course, they should have just let them adopt, but hey, you can't make somebody be a school teacher or administrator either.

If you have a note from your doctor with a diagnosis, there's little the school can do except to accommodate you

A professor friend of mine has made all of his tests untimed. And with that one move, he took away "extra time" as an advantage that students with affluent and savvy parents could purchase.

Here's the end of the WSJ article:
"A couple of years ago, administrators and teachers at Tarbut V’Torah Community Day School in Irvine, Calif., noticed that students they had taught for years were coming in with doctors’ notes saying they had learning issues and needed extra time on college-entrance exams. The school pushed back. “Parents want to do what’s in the best interest of their child and want to provide them with opportunities and support,” said Jeffrey Davis, head of the school, known as TVT. “They talk to their friends and their neighbors and realize their kids are getting extra support and that they might be able to get it, too.” The diagnoses sometimes didn’t mesh with what the school and teachers knew about the students. Believing that what was going on wasn’t ethical, TVT last fall brought in an outside specialist to review each case. “They are going back and looking at this thing and realizing that some of this stuff is baloney,” said Lee Weissman, a Jewish-studies teacher at the school. Mr. Weissman said private schools face an inherent challenge in pushing back against parents demanding special allowances. “What we are selling is college admissions; that’s what parents are buying,” he said. “When they are getting accommodations, and that’s going to be helping to provide the product you’re selling, it’s hard.”"

how many of these kids have the same doctor

And one of the reasons IQ tests have time limits. It does show you something.

I should say, I never felt the SAT was a type of test that didn't give you enough time. I never remember time being a factor when I took it except for possibly going back and checking your answers.

I think it tests ability to read, follow instructions, and use deductive reasoning skills.

And I'm one of those folks who are like you in that I test well, or at least, I don't get flustered taking a timed test. I'm both proud of and resent being told I 'test well'. I'm not stupid, I process the questions well and select the correct answer more often than not. That takes skill.