I'd be inclined to argue you need both.
If you have healthcare that's not tied to your employer, you are more free to change jobs. However, companies continue to prove they will only pay the bare minimum for menial jobs, like sanitation workers and service industry positions. As they already pay the minimum mandated by law, I would find it hard to fathom it turning into anything but a race to the bottom if the minimum wage is abolished.
But it’s not the 1970s anymore, people can get on the internet and find out what jobs pay.
You're not wrong, but this has not solved the issue of menial labor jobs not paying anywhere near enough for people to live on without assistance. Logically, it should work, but in practice, it doesn't.