I don't think you're actually arguing that programmers get paid too much.

You are arguing that dishwashers get paid too little. Your argument is that dishwashers produce a lot of value and you're right about that. The restaurant is willing to pay probably as much as $50/hour for a dishwasher if not more. The problem is that people are willing to take the job at $15/hour so there's no incentive for the restaurant to pay more.