So if it's not a question about loyalty/commitment, why does the rule exist? What's the meaning behind it? There must be some history, something happened in the past that required this rule? Or has this rule been in existence since the conception of LL?
I've already alluded to why I thought it wasn't allowed. Conflict of interest is one. Taking a roster spot from another deserving player is another. Setting oneself up for a significant advantage is a third. Such a wide open policy would come with too much baggage.
There's also an issue of fairness and equitability. LL Baseball is set up such that all players have essentially the same basis for play. Why should your child be given the opportunity to play on TWO teams for TWO leagues in TWO districts, when the overwhelming majority of kids don't get that same opportunity? Is it fair to them that they are "stuck" in one league because their parents live together? Why should your child get the chance for more play time, for more success, for more accolades, for more recognition than the typical LLer?
This isn't just a LL thing. I'm sure there are other youth sports organizations that won't allow it. Can a kid play football for two different Pop Warner teams? I doubt it. I'm guessing the same is true in Dixie Baseball, Cal Ripken Baseball, PONY softball, etc.