Yes. Anyone willing to work 40 hours or more a week and not leech off the government should be able to afford basic living costs regardless of whether they are an uneducated fool or not. Do you disagree?
Depends, and a real policy examination requires analysis of societal and governmental standards of "basic living".
Ex.
What are you defining as "basic living costs"?, because that has changed a lot over the years. Are you including just food & housing? Any sort of daycare? Medical insurance? Savings? A vehicle with insurance? How many sets of clothes? These are all questions that would have been answered very differently when minimum wage was introduced.
Let's just look at housing for the example.
A "home", in this case I assume, means a dwelling that would pass occupancy approval by the relevant legal body. As we continue to demand more, those buildings become less plentiful and more expensive. Yes, they are safer and higher quality.
The key point here is the effectiveness of a wage to provide this good changes not only due to the wage itself, but also by how the good is altered within the market and the governmental regulations at work.
A poorly insulated large room with a coal stove for heat and no indoor plumbing would not pass an occupancy inspection in most of the USA today, and therefore, is not available on the market at all. People in the past who received a low income and could not afford more would now find themselves homeless instead, but might have the exact same job making the exact same (inflation-adjusted) pay.
Someone with the exact same job today, to meet the same standard of self-support, would literally have to be paid far more for the same work (in real terms, not just inflation-adjusted terms) that established this principle in 1938.
After we do this (determine what "basic living costs" EVERY job should pay), I'd be curious what you suggest employers do about low educated dangerous work. Tree cutting, for example, is among the deadliest jobs in the USA. What should they be paid if the person with the easiest, safest job in the nation gets a home, food, insurance, etc.? Pay them six figures or more?
How much do you think it would cost to have a tree cut down in that market?