I agree that people sbould be able to live comfortably with their job, even a low skill one. But the idea that raising wages will mean increase prices does check out though. That, or people with higher skill jobs will be paid less and then they will be the ones to suffer the most.
Imo, we should aim to make things more efficient, thus cheaper because they actually became cheaper. E.g. solving the housing crisis => cheaper rent. Public healthcare => cheaper healthcare. Better schools => better citizens that leave less trash around => less expensive trash management. More public transport, less need to buy or do maintenance to a car etc. And so on and so forth.
Minimum wages can't fix this problem (they can fix others), they're just a bandaid on a severed limb.