BMR isn't just about culture and diversity. It's about teachers and service industry workers and everyone a functioning city needs. The gap is so large between market rate and affordability, and there are so many richer people still wanting to move into SF, that it is likely wishful thinking that market rate development will be "enough" to solve the problem.
And that is the reason why the Yimby position is not an obvious choice. Cities need to negotiate with developers to have sufficient BMR housing to be functional.
[1] http://48hills.org/2017/07/18/scott-wiener-trying-undermine-...