You could already commute with cheap taxis (eg in the developing world). The more important thing is that people want to live in San Francisco, they wouldn’t be happy commuting from some far off place in the first place. And as stealth campers have already figured out, not a lot of places available to camp in your car even 40-60 miles out, so might as well be where you want.
But the idea that your car could just involve itself in traffic jams all day rather than pay for parking is interesting, it could also look for time limited but free parking and move on to somewhere else when that expired, which is more common outside the city. Heck, it could park at a shopping mall that doesn’t allow walk offs…because no one is walking off.
Already, though, you've got a budget of >$4000/mo for a more comfortable studio apartment.
It's far cheaper to live in an autonomous motorhome that drives around all day and happens to arrive at work just as you need to be there each morning than to rent an apartment in San Francisco. Driving about is probably cheaper than paying for parking too, especially if you deliberately head for the busiest traffic.