More practically, the width of even wide streets like Geary is narrower than the depth of a typical SF building - see https://goo.gl/maps/YbJmqxpgEW62. Roads overall take up a huge amount of space in a city, but no single road is all that much area. For instance, it looks like the right of way on Geary is about 110'. If it went the full length of SF (~7 miles), then the whole road takes up less than 100 acres. For reference, Park Merced is 150 acres.
It would be great if all the lightly trafficked side/residential streets could be squished from 60' to 40', you're talking about 50 blocks -> 1000' width, which is over 3 blocks wide and about a thousand acres, which is approaching the size of the Richmond district (and that's just if you squish in one direction). But you can't just pinch-to-zoom in real life :(
Yes. NIMBYism is entirely about public policy. The fact that the land in question might be publicly owned is irrelevant. If anything, publicly owned land should be more subject to NIMBYism. Public land does indeed belong to the citizens.