It does help show that you are talented in math. The MIT and I think the Caltech applications ask for your scores if you have them. It’s obviously more prestigious if you get a good score on the AIME and qualify for the next level up. (My son took the AIME at least twice, I think he got a 3 on the AIME - which was the median score the year he took it - and he didn’t get into either MIT or Caltech. He did get into Harvard and CMU.)