A few replies to this but I don't think you're far off either way:
1. The biggest difference is the LA area has had multiple major sport champions where MN hasn't. But much like LA, MSP has a lot of different teams to choose from given it's size.
2. Speaking of size, per wikipedia the greater LA area has a population of 18.3 million people versus MSP about 3.7. I think that desparity can account at least for some of the reason even poor teams in LA have a decent following. It's just a numbers game at that point.
3. The Twins need to win, yes. BUT- baseball especially has a politicing (maybe not the right word) side to it given there's no salary constraints. If you don't spend enough on players, you're more likely to not be as good a team and therefor not win as many games. Part of that isn't the Twins' fault (I.E. lack of a salary floor/ceiling), but the Pohlad's aren't/haven't done themselves any favors either and that in my opinion is what seems to be weighing on and driving us fans away from the team, myself included.