But it isn't. A fifth of the UK working age population, for example, is neither registered as unemployed or earning money. Most of them aren't homeless, or entitled to disability benefits and aren't registered as unemployed because for whatever reason they don't need the money. All of them would be eligible for basic income.
You can afford to provide much better support for homeless people (many of whose bigger problems cannot be addressed simply by providing them with a regular income) if your budget isn't being stretched by the need to subsidise the perceived basic needs of huge numbers of content people that aren't actually interested in claiming subsidies.
You can tax their parents and give the students UBI. The sick will cost anyhow. Or you can exclude students from UBI, that's what you are doing now. I'm not against either.
The larger point is that not only is the idea of a UBI decent and moral, because nobody should worry about being homeless or starving in a rich society, but because its much cheaper the the alternative! Only someone completely blinded by ideology (or somehow profiting off of the existing system) would argue that its better to spend $50,000 dollars a year per homeless person to manage shelters and run a bureaucracy if simply giving that homeless person $25,000 a year and achieves a better overall result.