This attitude, where it is assumed humans don't want to better themselves, is why the guillotine was invented. Remember to where a low cut shirt.
I have done minimum wage work, albeit a long time ago, and I can tell from personal observation that not everyone is interested in bettering themselves via hard work and initiative.
I have worked in jobs where some positions are piecework, you can look that up, and others minimum hourly wage positions. Would you care to guess who was humping it all day long? Which people thought up more efficient ways to do their jobs? It was the people on piecework.
I held both of those types of jobs in the same furniture manufacturer many years ago and the people in piecework busted their asses. Most, but not all of the people on hourly wage slogged the day.
Here’s another interesting aspect. When you have a bunch of people on minimum wage regardless of what it is, it’s easy to see that some people do have a work ethic and others work at doing the minimum. Which is really poor for morale because it’s pretty frustrating when you’re doing twice the work of the guy next to you and he’s collecting the same pay.
In your world, they don’t have to better themselves because their basic needs are provided for when they work ANY job. But yet you are saying that they will better themselves anyway? Sorry, not buying it.