Your reasoning is pointless. Neither are really getting any benefit from the system, and a 20 weekly hours job paying a MINIMUM WAGE isn't enough to make a living by any means and it's not an option for a common worker someone must be desperate to accept such therms despite getting a higher paid working hour. Besides, when a company needs someone working only 20 hours a week they are very likely to just sign in a temporary contract, common in retail stores during christmas season
The ones who got permanent 20-30 weekly hours jobs are a minority in specific jobs that pay more, like for instance fireman. My uncle is a fireman and the nature of his job make him work for 26 hours a week if I'm not mistaken. Those jobs that pays above minimum wage don't really need to pay a higher working hour for a part-time worker than they do with a full-time worker
My reasoning that people shouldn't work extra for free, but should actually be paid for the hours they work? Sure, whatever, if you don't mind working 48 hours and only getting paid for 40 that's up to you. I personally would never accept that in a million years though. That's the kind of thing we'd go on strike over in Europe.
Part time minimum wage jobs aren't for making a living solely off of that. They're for either students, who can only work part time because they're busy with school still, or parents where one works full time but they'd like some extra money so the other one does a part time job while the kid's at school or something. Or I guess also for retired people who'd like a bit more money on top of their pensions, my grandparents kept working part time for a good few years after retirement in order to afford holidays and things.