I suspect there’s a point at which lower and lower acceptance rates may cause students not to apply, perhaps students that the college is looking for. Stanford has jumped the shark, so to speak, as a viable option, and I don’t think I’m the only one to hold that view; there were internet memes last year joking that Stanford didn’t really exist and of course the NYT spoof piece on a 0% acceptance rate.
(I wonder something similar about UChicago RD, i.e., why bother. And Harvard? Please.)
I’ll have to think some more, but I’m not sure that not reporting is really beneficial to students.
In addition, if Stanford continues to report to the government, the rate will end up in the NCES website eventually anyway - it won’t go unnoticed.