I'm not sure how that is related to gentrification. And last time I checked, people are not homeless out of choice, but from socioeconomic reasons, mental health problems and just bad luck. I'd argue that rent control and housing stability can go a long way to mitigate those problems in the first place.

And you might be partially right, nobody likes homeless people. But for very different reasons. I don't like that society lets people fall, almost permanently, on the side line.