I've lived in east coast cities (NYC, Boston, and Philadelphia) for the majority of my adult life and while homelessness is less of a problem in the northeast because of the climate there is still a good amount of it in the major cities. I think it becomes way too easy to tune out those commentaries and avoid the parts of the city that they apply to.

In Philadelphia, I lived a few blocks away from the Girard stop on the L train. I would just avoid walking by the station because it was a hang out for homeless people and drug users in the area. Pretty much everywhere within a 10 block radius of the station is built up, there's always people out, and it feels like all of the local businesses in the area are thriving (more recently there's been too many chains opening up which sucks but I digress), there's barely any homelessness or crime with the exception of package thieves (I just bought a $20 box off amazon to put in front of my house and never had a problem) and the occasional car window being smashed.

In NYC, especially Manhattan although the same applies to the outer boroughs, unless you live around a more touristy area then you don't even think about it. In Boston even less so besides downtown.

I don't think trying to contain people to specific areas is a good solution. There's obviously a greater social issue across the US and other developed nations and it's a very hard problem to start solving, but I would guess that most cities continue to ignore it as long as its easy for the majority of the population to ignore it.