I don’t think the left is afraid of pissing radical feminists off. Also the left already advocates for at least some of the things you mentioned like mental health and homelessness. I don’t think those topics are particularly popular in the “manosphere”.

I think the main problem is the men invested in the manosphere want comforting lies and the left won’t give it to them because in reality it’s much more complicated than what any of the influencers say.