Do you think those that are too mentally ill, violent, or antisocial deserve to keep being displaced because they can't function in current society?

Giving more cash aid to those in need will solve a lot of problems (mostly for the first group), but as you say some of them (usually from the second group) are not able to use it properly. Those folks need support in the form of more services. Most of these services needed are mental health services.

These folks are in dire need of those mental health services; which can be very hard to get, even for those with money. It gets even more difficult if you need more than just a recurring therapy appointment, like being in a group home.

Some folks will even still hurt others with these supports, which I believe you referred to with violent/antisocial people. Those folks need to be rehabilitated. Unfortunately most of them will end up in jail or prison, which in its current form will not help them unless they put in a LOT of work to break the cycle. (There are still people that I believe will never be rehabilitated and should be in jail, but not in an environment like an American jail.)

Do these people deserve to be pushed out?

I do understand the desire to keep folks from sleeping on benches, making things smelly. Truly. But displacing this population so you don't have to see or acknowledge their existence does not solve the issue. We need to look at the issue and work together to demand better for our more vulnerable populations.