don't they choose to live in SF because that's where they got the job? if they would move they would lose the job, because you generally can't take your job with you. (remote work being the exception)
if life in a place is expensive, and jobs in the same area do not pay enough to cover those expenses, then a person with that job in that area is poor.
I don't know whether you've been to San Francisco, but most (about all?) people who can get a 100k job in SF has quite a bit of mobility w.r.t. where they could live or who they work for.
I would love to see a sample of a handful of cases of these 100k earners who we should consider poor and in need of assistance to make ends meet.
how long would the commute be though. if you have to spend more than two hours commuting each day in order to afford living with the money you earn in SF then i'd see that as a problem.
Within 1 hour commute that you could live comfortably on 100k:
- East Bay (El Cerrito, Richmond, Concord, Walnut Creek, Martinez)
- North Bay (Petaluma, Novato, Vallejo, Santa Rosa)
Within 90mins:
- South Bay (Milpitas, South San Jose, Morgan Hill, Gilroy)