For another anecdotal data point, I grew up in LA, moved here as a teen, and have spent my career here with regular visits back to LA, and haven't found that to be the case. Leisure is so much _easier_ in San Francisco that it's hard to avoid it... Every resident is a maximum ten minute walk away from a park, there are constant awesome free events, and your life isn't fully governed by the dictates of constant traffic between any two points in the city. I've spent my time in the city itself but I've had plenty of exposure to different parts of the Bay and, controlling for the fact that it's less dense, much of the same applies.
The sheer success of the metro economy relative to LA over the last ten years means that there are a lot of people who moved here with dollar signs in their eyes, and I don't doubt that that's shifted the culture a bit, but it's very easy to avoid IME.
Our data points do differ in that it sounds like you're primarily around families and I'm around single people or young couples. Perhaps what you're describing is true for that subset of the population.