I find the title 'minimum wage' is offensive in itself and implies for some what the OP has said. It needs changing but guess even then it will never remove the stigma.
Saying that, I agree that some people have a bad work ethic and it wouldn't matter what they were paid.
I'm low paid but love my job and give extra time for my own satisfaction of doing it to my standard. I live within my means - but my parents modelled this to me in my upbringing and I've found as the years go by this is dwindling - some of the younger generations increasingly don't have good work ethic/budgeting modelled and it affects their attitude. I'm lucky that I work with like minded people and it makes a big difference (small family firm)
It's interesting though that when you look at motivational factors, pay is one of the lowest priorities. As new staff join us they have often been better paid but prioritise 'nice' friendly colleagues, working atmosphere, a bit of flexibility when needed, responsibility at their pace etc
I wonder what some people's pay would have been if it hadn't been introduced, so think it's probably been introduced for the better in some sectors.
I also think it's relative too; you take a customer facing job then your 'basics' are smiling, being polite/helpful etc which your wage is paying you for. In something like 'warehouse' the 'basics' are completely different. On the flip side, I think the basics from an employees POV is respect, polite, good working conditions etc
I also think the old philosophy of cut your coat according to your cloth has gotten a little lost and what were considered luxury items of purchase are now considered by some, essential which impacts on wages needed. The last housing boom when prices went crazy is still impacting on people's lives.
There are just so many factors at play in defining the wage.
Don't get me wrong, NMW should be more, but for some small independent/family businesses it's already putting them at breaking point when you add in their rising business rates, utilities etc.