Remember kids, minimum wage=minimum effort. Never give more than that. You're employer paying you minimum is literally telling you that if he was legally allowed to, he'd pay you less.
I think you really nailed something there... We don't really have a minimum wage, we have a minimal wage.
A proper minimum wage should be pegged to the cost of living - it's the minimum required to live. Instead, what we've got is companies paying the absolute least that they're required to, and lobbying to keep that number as low as possible regardless of the cost of living.
Minimum wage limits need to be set by an NGO independent body. The UK uses a living wage criteria. My opinion that even the voluntary real living wage is set too low atm. This also does not take into account for the rent increases that are hitting kids due to interest rate rises. Even so, I still see this as a massive leap over the shambles that the US is. The current government is trying extremely hard to implement US limits in the UK.
Switzerland doesn't have a minimum wage either, but the problems aren't as dire (yet). Several cantons have however now introduced minimum wages and these are inflation adjusted, so a lot more future proof. Also they don't need to be renegotiated again and again as the law doesn't expire. I only see them disappear if we get a nationwide solution that replaces the local ones. But I agree with you: They are now set by the legislature and arbitrary and they should be informed with NGO data.