Unpaid house work isn't going to get worse if women get the (new) option of leaving situations they previously were stuck in.
The problem of unpaid "emotional work" is caused by a sexist society. More social safety net either does nothing to alleviate that problem, or it helps. It makes no sense to argue it makes things worse. Unless you provide even a shred of an argument for how it could make things worse, it sounds like you're just yelling into the void of the internet. Unless by "men are impossible to talk to about this" you really mean "men don't accept my assertions on faith".
Edit: Also, it sounds like possibly you don't know what basic income is. Or you mean something different by it. This[1] sums it up neatly in the first paragraph. I'm not trying to be insulting, it just sounds like you're talking about something different.