I don't think many people would argue with the evolutionary nature of cities. I think what people would say, however, is that when cities change those with the least economic muscle tend to be the most adversely effected (e.g they lose their homes/tenancies when they can't afford to pay inflated rents).

Again, that in itself might not be a problem if there were other places to move that poor communities could afford and wouldn't detrimentally affect their lives.

I can speak from experience in London, poor communities have NO WHERE to move if an area is gentrified and they are forced out. Prices are city wide too high, gentrification has left no where 'cheap'. What that means is moving further from central London, which means moving further away from the main source of work and increasing expense of travel. Which all in turn means an even greater slip into poverty.