I think all full time jobs should at a minimum pay a true living wage where one can live comfortably, save for emergencies, etc. If the job cannot pay that then it shouldn't exist.
There are many ways to accomplish this beyond simply raising wages. Better government programs, lower the cost of housing/medical/transportation/food/etc. (these are surprisingly simple but many vested interests don't want this to happen), better retirement programs, etc. etc. etc. You see more of this in more socially democratic countries.
I’m not against that idea but there are some knock-on effects we should be careful of. For example, it will make it hard for younger people to get a job. If I have to pay a teenager the same as someone with a decade or more of work experience, that teenager probably won’t get a job.
With a lot of these discussions, we need to be careful about the seductively simple solutions.
If the minimum was the actual minimum, then why would the person with a decade of experience ever work for it?
The issue of "which jobs should exist" should be left to the market only. If typical low-end jobs throughout the country pay wages that do not guarantee a minimum living income, the government should simply make up the difference for everyone in a fair way (subject to clawback rates as earned income increases, in order to keep the overall arrangement viable).
(Lowering the cost of essential goods and services is also something that can be done by leveraging the open market. It doesn't take yet another wasteful government program, which is the typical approach in socialist and social-democrat countries.)