However they do offer a "Landscape" which provides similar details and many admissions programs use that to do something like what you're describing.
But that certainly isn't scalable. I'd argue the SAT is one of the most fair things we have at scale.
It's true that the SAT used to be biased (for example the word problems would use the word regatta which a wealthy east coast teen would know but a poor west coast teen would not) but from what I've seen they've done a good job removing that bias (as shown by this paper).
Admissions officers could then watch the recording, or rely on the automated scoring that the AI platform spits out.
Not everyone performs well on interviews, and I imagine performance would vary even more on interviews where you know your "interviewer" is an AI. But it could be really interesting, and a way to achieve the type of personalization and scale that you allude to.