How important is a good AIME score for college admissions?

I only recall MIT asking specifically for AIME score. I don’t think my son had one until after apps were submitted Sr year, although I tend to confuse all of those competitions acronyms. (USACO, USAMO, NACLO, etc)

IMO, it is just one more EC. A measurable one, but it won’t tip the scales on its own.