Most cities are run by people who would call themselves very progressive, and have been for a long time. New York, SF, Chicago, LA, and other big cities have all had 100% progressive leadership for a very long time. These same cities, which purport to have "fair" "progressive" policies have huge problems building affordable housing (mostly because they want to regulate its construction to hell). It is not due to conservative opposition, it is generally due to opposition from the left, often on grounds of "avoiding gentrification" and "keeping the character of the city."
Look at Calle 24 in SF for a good example - in order to preserve diversity, a progressive organization has blocked a lot of projects that would add low-income housing to their neighborhoods. In addition, progressive mayors and city governments make it comparatively pleasant to be a bum in these areas - you can do whatever you want, including committing petty crimes, and you will get generous amounts of money for it. Economics 101 tells you that when you subsidize something, you get more of it. It's true for solar panels, and it's true for homelessness.
By the way, what happened in the 80's in NYC is that the professional class had enough and started electing conservatives. Those are the people who actually cleaned up the city by forcing homeless people to take shelter beds (they often don't want to end up in shelters because shelters have strict rules), and making it unpleasant to be homeless. At the same time, they invested in things like brighter lights, subway cleanups, and other nonsense that improves quality of life (but is not "fair" according to progressives). They also empowered police to enforce criminal laws on petty criminals.
So yes, this is a problem with politicians who claim to be progressive. I used to call myself "progressive" until I learned that this is where "progressive" politicians lead things. As a progressive yourself, it's up to you to call this behavior out if you want people to think that your ideology actually helps people.