Best I can tell, the best good-faith summary of the progressive stance on housing/gentrification would be that we can't afford to wait until supply & demand sorts this out. If most people can afford up to $1500 rent, but the cost of the median unit has gone up to $4000, realistically in the very best case scenario it might take 10-15 years until supply increases lower the median price to that level. And there are people hurting right now so we can't afford to wait that long.
Granted, I've never actually heard anybody say that, but that's an intellectually honest claim that seems in line with their views and that I think that is reasonably true. If they would say that, and they would commit to increasing supply in the long term in addition to proposing short term relief measures, I think we could have a much more productive debate.
The frustrating part is that what the vast majority of these people actually say, is that supply & demand have zero bearing on housing. And they've been saying this for decades. Failed progressive policies are a big part of why we have a housing shortage.
It's like if there was a small spark of a wildfire, and I were to claim that water won't work, we better just wait and see what happens. So we wait and let the fire keep getting bigger, and keep saying water won't work. At some point it actually becomes true that water alone won't work, once it is so far out of hand that there's possible way to deploy enough water to bring it under control. But the takeaway for the next time there are new sparks somewhere else should not be that water doesn't work!