Having to work too many hours due to a low minimum wage is a common reason low earners don't have the energy to try to study and move up the ladder. So I agree, removing the minimum wage doesn't sound like a good answer at all.
It's all well and good to want to study but for some their are many roadblocks. Not all bootstraps are made at the same length and some are just a little too short to reach.
Working is studying to move up the ladder. There's a reason a senior developer makes more than a junior developer. Even if you work a completely no-skill job doing something like sweeping floors... if you show up on time, work hard, etc. you will get references for better jobs with more opportunity to grow. Or perhaps if you do a good job sweeping floors, maybe you'll get the opportunity to get promoted to working the stock room, and then managing the stock room, etc.
It's all well and good to want to study but for some their are many roadblocks. Not all bootstraps are made at the same length and some are just a little too short to reach.