I think that's a pretty fair assessment of the local teams. I'd say the Timberwolves are similar to the Twins in that regard, while the Loons and Lynx are similar to the Wild - a passionate niche fanbase, just with a smaller niche than hockey.
Based on how you laid out the LA teams, it seems to me that to get sustained passionate support two ways: service a passionate niche, or have a long run of sustained relevance. You earn that unconditional support that the Vikings, Dodgers, and Lakers (and USC football) get. Those teams aren't all pumping out dynasty after dynasty (I suppose the Lakers kinda have), but they don't have sustained stretches of irrelevance either. The Clippers were run like a dollar store for decades, and their interest relative to the Lakers reflects that. They've actually been pretty competent lately, and they're still just beginning to develop that goodwill with fans. And you can't get much more irrelevant than ceasing to exist like LA football did.
So yeah, it is a tougher job to be an owner of a team that doesn't get passionate engagement win lose or draw. But that engagement doesn't just get bestowed upon certain franchises, it gets earned with competence over time. New owners would have some work to do to earn that for the Twins