I think you're making the assumption that the person you're talking about would get the job without being out-competed by someone else? Higher paying jobs have more competition.
Relatively higher paying jobs have relatively more competition. The lowest paying jobs (minimum wage) will always have the least competition.
This does not seem to be a universal truth. Time and again I see news stories of grocery store type jobs (or McDonalds) getting hundreds of applicants.
That's because the minimum wage is higher than the market value for many of those people's productivity. Without a minimum wage anyone willing to do work would more quickly be able to find paying work. And anyone who is productive will quickly move up the pay scale.