Does everyone deserve the same though? Because 'everyone' includes rapists, child abusers, violent thieves, as well as people who just don't give a shit about anyone else and wouldn't be prepared to do a days work if they could have the same standard of living thanks to other people's work.
I don't believe that everyone does deserve the same. They deserve 'enough', but not the same.
I wouldn't give up ownership so that everyone could be housed, and that's not because I'm selfish, it's because I already contribute time and money for the greater good in the form of voluntary work, taxes and financial charitable donations. I might have the same security if housing was distributed in the way you are suggesting, but what about everything else you would be taking away? Like a sense of achievement, pride, the freedom to have a property that best suits me, my work, and my family? Don't get me wrong, my owned house is tiny and I think my family would be much better off with a bigger one, but actually, I don't want a bigger one that isn't our own. If the government was going to give me a home, then I'd be entirely dependant on them. I would have nothing to sell if DHs work took us to another country. That would leave us less secure than we already are.
I agree that more community projects would be good, for more reasons than just nice housing for everyone. But in a free country I expect the right to be able to choose the cause I help for myself. It works better that way because if people are working towards something that actually care about, their work is likely to be more efficient and more productive.