No, I wouldn't.
I was an NCAA athlete, and I did transfer once. (It wasn't for playing time as I was in an individual sport)
It has a major down side for the athlete and for the teams that are destabilized. It has negative effects for the university, the fan base, team culture, and many other things. I've lived it. I had great success at my second university but I still wonder if it was worth all of the downsides.
I think there should be some freedom to move around, but also that there should be limits placed on that ability.