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At $20, you'd earn a roughly $40k salary if you were to work full-time. That won't buy you a house, but it will let you rent a room in a house within commuting distance from your place of work, maybe drive an old beater Camry, cook your own food, and have some money saved up for school.

Why not $50, that's a $100k salary - most people would be opposed to it because you'd be able to potentially afford much more than what they perceive a fast food worker should be able to afford.

Do we have logic behind why they chose $20 and not $50?

You pay $7 for a burger now? Why not $15?

I mean, if the customers won't mind, and agreed to pay much more, the wages could also grow much more.

Why are you pulling random numbers out of your ass? If a worker makes 60 burgers in an hour and they are paid $20/hr then that adds 33 cents to the price of a burger that assembles itself. If they are paid $50/hr then 83 cents.

Math isn't hard and politics poisoned your brain.

Except it is hard to imagine there to be enough demand all the time to sustain this for every hour they work, and even in case there is, they would be happy busy making so many burgers for maybe eight hours in a row each day. And let's not ignore that making food is also not the only work for those working in a restaurant.