I don't think I'd want my u12 on the u13 team full time, but he will be playing with them for a few games for the experience of 11v11 and for more game time.
In North Carolina* there are a few of these programs that have youth programs and USL teams. I don't think they have near the levels of support and engagement that you'd see in Europe for a 2nd and 3rd tier teams.
I've been to a few NISA Stumptown games waiting on MLS to show up and that team has affiliations only with youth teams and is stand alone.
* Charlotte Independence goes up through to USL 1
* NC Fusion USL 2
I'd be very interested in similar for boys - one of my major complaints is information asymmetry between the clubs and parents and the difficulty in finding quality information.
(Based around Charlotte, where there is no forum dedicated to youth soccer)