Some homeless people are mentally ill but this isn't a reason to not have a social safety net. There used to be a term 'noblesse oblige' where the more fortunate are duty bound to look after those less fortunate, to my mind this is where a social security net is required.
Some people will for one reason or another, whether by bad luck or plain old stupidity will end up at some point in there life out on the streets. If these people have kids then the kids end up on the streets and no longer receive an education, so they'll end up as criminals or on drugs or something like that. If this cycle is allowed to continue you end up with large areas of slums in cities. If instead when bad things happen there is a security net that allows you to wipe yourself down, get up and move on then the cycle is avoided, or at least it's depth is less. It can become a social welfare problem, but at least you don't have children dying in tents from exposure, and there's always the chance that when things pick up, they'll be able to get a job or at least the children do.
Some people will for one reason or another, whether by bad luck or plain old stupidity will end up at some point in there life out on the streets. If these people have kids then the kids end up on the streets and no longer receive an education, so they'll end up as criminals or on drugs or something like that. If this cycle is allowed to continue you end up with large areas of slums in cities. If instead when bad things happen there is a security net that allows you to wipe yourself down, get up and move on then the cycle is avoided, or at least it's depth is less. It can become a social welfare problem, but at least you don't have children dying in tents from exposure, and there's always the chance that when things pick up, they'll be able to get a job or at least the children do.