Cal Tech also asks and and MIT does, so you can guess their importance. It doesn’t mean that it’s a requirement, but there’s no way for these schools to differentiate among the many 800s in Math and Math 2 subject tests they get.
“Some are on hs teams (eg, math team,) that go to regionals or better.”
These math teams are typically formed by how kids did on the AIME or AMC.
“If it’s a holistic college, it’s not about better or more awards. No boost.”
I’m not sure you can absolutely say no boost, making the Olympiad is a boost, maybe it’s not a hook as professorplum noted, but people that are on AMO do well with the MIT, Stanford’s of the world. It is not causation but it is correlation.
Stanford has hosted the AIME, why? From their website:
The Stanford Math Circle, in cooperation with the Stanford Math Department and the Stanford Pre-Collegiate Studies Program, will once again be offering the AMC 10/12 contests to Bay Area students who are not otherwise able to participate…most high schools, and even some middle schools, already give the AMC contests. We would like to make it possible for everyone to take these contests.
Make possible for everyone to take it, because Stanford has the same problem that MIT, Cal Tech has, they cannot distinguish between the top students at least to wrt math capabilities for their stem programs. Stanford also hosts math contests, they like them and the message is they want high schoolers to take them.