There appears to be this underlying assumption that students transfer schools for no reason other than athletics. Is that the motivation for some transfers? Sure, but there are a lot of kids who move for reasons other than sports. But there are also kids who move from district to district because their parents get new jobs or because they're renters who may not have the luxury of staying in one place for a long time. At one point in my childhood, my family moved four times in five years.
How do you draw a distinction between students transferring for athletic reasons and those transferring for other reasons? I can only imagine the amount of money wasted on "investigating" high school transfers.
By attempting to stop students from transferring for athletic reasons, you're inevitably going to penalize kids whose transfers have nothing to do with sports. You're cutting off one of the avenues for them to build new friendships as well as whatever other benefits you think sports confer on children.
I think some of the main reason, and its the reason I like the no transfer rules is keeping High School sports about the school itself.
What is the school itself? The building, the teachers, the parents? Adults who base too much of their self-worth on success in children's sports? High school sports should be about the students, not institutions.
As an admittedly extreme example, ask Penn State or the Catholic Church about what can happen when you prioritize institutions over individual children.
What about the kid who is good enough to play high school basketball but gets cut from his team due to other players transferring in. Will he now have to transfer? Can be a long cycle.
Of course he doesn't have to transfer. High schools are supposed to be academic institutions, not athletic programs. You don't have to play a sport to get a high school education.
If your kid gets cut from a high school team, then he probably doesn't have much of an athletic career beyond high school. But if it means that much, then fine: find a new school. I prefer that to taxpayer dollars being wasted--directly or indirectly--on investigating the validity of the reasons for a kid transferring high schools. Step back and consider the absurdity of that.