It is pretty common here. There are a few gyms that only compete one or the other, but most do both.
I don't think it gives an advantage in moving up in levels. If anything, you spend more time practicing routines instead of just uptraining. The one gym near us that only competes fall for compulsories seems to move up girls one level a year for the most part.
It also gives girls who aren't ready by fall season a chance to compete in spring if they weren't ready by fall.
Some gyms use spring as a tester season, so girls do spring in new level, then train all summer same level and they rock states. Then new level in spring again if they are ready.
Basically just different gym philosophies at play.
My daughter started competing at 6 and has repeated levels 4 and 5, and is doing 7 again this year as an 11 year old. She always competed in fall and spring meets, though not always a full season of one or the other.
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