Yeah, the buildings aren't very tall, but people are in them right now.

Before you can build a newer, bigger building, you first need to buy a large enough contiguous area from potentially several owners who don't particularly want to move. That adds friction and years of extra work to any new building, which will discourage new construction, lower supply and raise prices regardless of the zoning.

Unless you're proposing that the government begin seizing tracts of land in Manhattan on behalf of high-rise developers?

I don't think this is as much of a problem as you are making it out to be. If the east village, which is currently mostly zoned R8B[1] were tomorrow to be substantially upzoned (to say R10) you'd see lots of new construction within a year. There'd be so much money to be made that deals would happen.

[1] http://www1.nyc.gov/assets/planning/download/pdf/zoning/zoni...