In the end it all comes down to money.
If the parents feel it is worth playing the additional tuition plus time and cost for the additional travel, and their kid is good enough to play AAA, then they should sign up for AAA. If the parents don’t want to spend at least twice as much money and spend all their free time on the road, then there is no reason not to play AA instead.
Then you have the parents who are willing to pay for their kid to play AAA, regardless of whether or not their kid is a AAA player talent wise.
If a program doesn’t have enough kids to field a AAA team, but they are willing to play AA, then they should be able to play AA.