TL:DR version – actually, that's exactly what socialism means.
The problem is that socials never figure out where the money for a living wage comes from. Higher wages means higher costs. Higher costs mean you need more for a living wage. Eventually you have to tax the wealthy to pay the poor.
Socialism is a system of collective wealth. I'm not saying we take everyone's money, put it into a pool, and distribute it based on how much/how hard they work. I'm saying that if someone is working 40 hours a week, they should be able to afford basic living expenses without welfare. I'm also not saying that cashiers/mcdonalds workers should be making the same as teachers or EMTs or trade workers. Those people (and many others) need a payraise, too. There's no reason someone with a college degree should be living paycheck to paycheck or even less. And no, I don't give a damn about "small business owners", because I f@%king am one, and if you can't afford to pay a living wage, you can't afford to stay in business.