"Other people's money" of the rich is most commonly the surplus value, i.e. our money that were taken away.
But without going into semantics, most people live in financial conditions that don't allow them to be so generous, or else they risk losing everything themselves. Those holding billions will not suffer much spending large money supporting the poor. It's just not correct to draw parralels.
If I'll give enough money for someone to live through a week, I'll be left broke and won't be able to pay my rent and food. If Elon Musk would do the same, he wouldn't even notice.
Yes, homeless are normally forcefully pushed out of wealthy areas, because they interrupt scenic views of places where the wealthy isolate themselves from the horrors they cause.
And shelters should be funded on the federal level, from a progressive tax, not by municipalities.