There's also nothing that says you absolutely have to stay in the Bay Area afterwards. Many founders head back to where they come from if that's the right thing for the business.
There is a method to the madness. They have proven it.
If you want to be in fashion-tech, for example, you want to be in New York (or possibly London). And, there are lot of other industries concentrated in specific areas around the world.
Limiting to San Francisco is limiting your industry. Sure you can get a ton of web developers, but you'll lose access & relationships to the REAL industry insiders that matter for your vertical.
To know whether remote will work YC needs to try it.
(Mind you, even with YC's intake, it's likely you'd never see a statistically significant result either way. There's too many variables and not enough samples.)