"socialism ultimately fails because it runs out of "other people's money"
Yes, but when only a few people are able to hoard most money leaving little to others, suddenly some kind of "socialism" becomes appealing to the large number of people left with too little to live well enough, especially when they can't pay for basic needs like healthcare or education.
Sure, socialism usually doesn't solve those problems because it again creates an elite which hoards the money and leave little to others as well, so it will ultimately fail.
There's a third way, of course, but it anyway requires powerful, rich people to be less greedy, and understand some wealth has to be shared to create a functioning society. They can choose to share it through labour and wages, or through taxes, or a mix of them - usually, the best solution to avoid "socialism".