Sure, it seems a noble aim. But I could throw that back at you, and say, what on Earth is the problem with saying to people, "
Sure, we'll give you a home and enough to live on. And in return, we expect you to be available for a certain number of hours per week to do some useful work the benefits other people.", which is what my alternative proposal would amount to. I really don't understand why anyone would object to that.
btw on making sure, no-one goes homeless, I'm pretty sure the way to achieve that is to - ummm - build enough homes for everyone. As long as the UK does not have enough homes for everyone to live in, then it's inevitable that some people will end up homeless. That once again is basic laws of mathematics - and no level of UBI is going to prevent that. If you think you can prevent homelessness by handing out free money to everyone, while not dealing the the problem of, not enough houses, then you're looking at the wrong end of the problem!