Get there
... in the same condition you started out in!
That's #1
"Why is that?" That's a good question - because they can, eh? ...and there is precedent.
I'd be curious to know if it's same in New York City? How about ultra right wing backwood type places where there are not any bicylists (and any who show up are considered deviant)?
I don't spend much time in SF, but in Berkeley, pedestrians will stride out into traffic without being CERTAIN that vehicular traffic is not a threat; there is a "trust" that the drivers will not kill or hurt them! Watch 'em; many peds don't even look.
There's more to it I suppose, like the balance between behaving as if vehicles represent a DEADLY threat and exerting some claim to OUR road. What the OP describes is the balance tipped way over to the "claim" side.
I don't always stop at stop signs - I can see clearly that NO traffic is approaching OR stopped at the other three (or two) legs of the intersection, I breeze it. Lights are a different matter, for me.
If there is traffic, I don't proceed unless there's eye contact AND it's my turn. Often drivers will "wave" me through (usually after waiting me to a full stop when I'm obviously stopping and they could've got the hell out of my way already, and they have the right of way, oh well); nothing doin' pal! I go when I know that it's safe, not when you say so, especially if you "made" me stop, or, I'm already stopped.
One more thing - I do make an effort to acknowledge what I consider proper respect for me as user of the road. A nod, salute, wave, smile, some indication that I appreciate the hesitation to pass until safe, allowing a few extra feet, the eye contact, etc.