I second @theloniusmonk. Many kids score 800 on Math Level 2 (21%), yet only 2.5% (AMC 10) or 5% (from AMC 12) of participants qualify for AIME. The median AIME score is usually 5 or 6. Scoring 6+ indicates strong math knowledge.
Team results often reflect the performance of the strong team members, especially in competitions like ARML where team has 15 members.
As mentioned above, there are at least a few schools that pay attention to AIME scores. CMU is also one of them.
Just this past week my two kids received a college mail from University of Michigan that specifically talks about their outstanding performance on AIME (10+ in their case) and invites them apply to the honors program in mathematics at LSA and to look at their several scholarship and grants. I am not sure if my oldest got more AIME related college mail in the past, but since this was the first college letter for my rising sophomore, I actually read it 
At the very least it shows, that some universities consider it worth seeking students that perform strongly on AIME.
Bottom line, if you are applying to any of the schools mentioned above, then AIME score will be considered. If not one would hope a strong AIME score will be helpful, and USA(J)MO participation will make one stand out.