I forget the exact levels, but it's something like this with completely made up numbers. (I could look it up, but I'll choose numbers that sound reasonable to me for the US)

Ages 15-18 - 7.25
18-24 - 12.00
24+ - 15.00

There are generally some tradeoffs between hiring younger people. Laws against high school kids working past certain hours on school nights for example. General attitudes about work ethic and calling in.

As a previous manager of what would typically be a minimum wage like job, I would gladly pay 12.00 an hour for a young adult over 7.25 to a high school kid working his first job. Because typically the reliability and job performance is going to be better, and worth the extra money. The business as a whole will run smoother.

When it comes to 24+, It may be tougher to defend a higher wage at least in my business experience, however there are certainly people that I would have gladly raised to 15 an hour as to not lose them. However, I didn't have to so naturally I didn't.

Should people 24+ be stuck in entry-ish level positions to where 15 an hour is a good pay scale? Probably not. However there are millions of people where this absolutely applies, and without marketable skills, in combination with less than perfect prior life choices leaves them without much hope to find something better.

You can say they could get loans and go to school, but in my experience there is a LOT of people where basic addition and multiplication skills are literally non-existent, and do we really not have the resources in this country to enable these people to earn a bare living outside of poverty levels? Not to mention, many of these people are attempting to support kids on these levels of income.

It's a hard set of circumstances, and you can absolutely find evidence to support both sides, and I'm not one to be finding the solutions to these very difficult questions.

However, I do believe as a nation we have the resources to supply everyone with a decent level of independence without the need for government handouts. While at the same time, I believe that if left completely up to the market, it's eventually going to lead to (and already has) people being left behind.

Eventually, robotics and AI is going to take all these jobs, and probably even many of the jobs that you aren't suspecting will be. Not necessarily in the next decade, but in 20 years? 30? This is getting out of the scope of the minimum wage argument, and more a philosophical argument about what society as a whole can/should do for/with these people. Because eventually the minimum level of job required for humans is going to get higher and higher and will leave a lot of people on the outside looking in. To a much larger degree than is already happening.