And several developed countries have no floor other that agreed by through collective bargaining.
https://www.investopedia.com/articles/investing/080515/5-dev...
This isn't a matter of improving the situation for everyone, it's a matter of improving the situation for the majority of min-wage workers.
If someone genuinely can't provide $10/hr of value, then either 1) they need to upskill (and there are social services for that, although perhaps not in the US idk) or 2) they're like one of those literal retards who are becoming literally unemployable, and the solution is either to subsidize their employer (which is okay in this instance because you're not subsidizing a race to the bottom like you are with subsidizing normal e.g. McDonalds wages) or put them on a disability pension.
But realistically, most people are capable of upskillinng and that's what they should be doing if they're not valuable enough to an employer.
There are many people coming up with solutions but clearly 'free market' adjustments have failed an increasing number of workers.
But I will disagree with your economic value question, I think service workers are undervalued greatly.
There is a giant disconnect between wage and economic value, the market is terrible at connecting the two.
If you set the minimum wage at $15/hr and do nothing else, you have made that person worse off than today. Everyone around them now has more money, so everything is becoming more expensive. They now can’t find or keep a job, because any employer who employs them is losing at least $200/week, $10K/year by employing them.
I don’t know what the optimal solution is, but it’s not clear to me that the above is it.