It'd be really interesting to see what would happen - for instance, what fraction of players would pick each pool during the first few weeks after launch, and then how many of them would switch after? What about players who joined a few months or a year after launch?

Unfortunately, pretty much the only company that could make this work is Valve, because they're the only one who actually cares for players and is big enough that they could gather meaningful data. And I don't think that even Valve will see enough value in this to dedicate the substantial resources it'd take to try to implement.