Obviously, no one (sane) is going to be in favor of #3. And while many people claim to want to keep things the same, as in #2, the amount of authoritarian city regulation necessary to make such a desire reality would be completely oppressive. It would require that rents be strictly limited, even when old residents moved out willingly and were replaced by new ones, regardless of their income. And besides just forcing new development out somewhere else--probably to a more auto-dependent, less environmentally and economically efficient location--it would discourage building owners from maintaining any of their holdings beyond the bare legal minimum. I encourage you to think through amount and complexity of city control it would take to actually make this work effectively; to do so here would require another post entirely.
The question of gentrification, as most of us know, is not "why do cities pursue it?" but "how do we maximize its positive aspects and prevent or minimize the negative?"
After all, contrary to Renn's assertions, cities don't have much incentive to gentrify. It's a terrible situation for the displaced residents--that isn't in question--but it's bad for cities as well. Displaced residents generally don't end up leaving and bothering some other city, they just end up in lower-quality homes, further away from work, school, and the social or medical services they might depend upon. Whatever those needs might be, they don't disappear just because the family moves a few miles away-- they just become less effective, and more costly to deliver. As even middle-income residents get pushed out of the middle of the city, increased prices push out beyond the city core, affecting everyone negatively. Except landowners, of course.
Reducing displacement is the challenge of gentrification, and thus far, no city has solved it in a completely satisfying way. That's not to say that some haven't been more successful than others though: even San Francisco, notorious for its out-of-this-world rents and home prices, is barely half the cost of Palo Alto ($835k vs $1.55m). At seven times the density, SF has done a much better job of facilitating growth than Palo Alto (although still a comparatively poor job), and this is certainly part of the reason it's not doing as poorly. But San Francisco also only grew by 30,000 people between 1950 and 2010; over that same time period Seattle, a considerably smaller city, increased its population by roughly 140,000. (Just for comparison, Palo Alto has increased in population by only about 10,000 in the past fifty years, although it's much smaller.) What Renn ignores, and what complicates the context of these statistics, is that demand differs between each of these cities, and responses will be, or should be, calibrated accordingly.
