You just hire another shlep who can wake up on time to hit the red button. If you can't find a reliable person to hit the button for you, you do the R&D to automate it.
As I understand it, your scenario is how unions justify their continued existence.
You're reading an argument that I didn't make.
If you're not already an American Republican
I'm a libertarian. I believe that if all you can do is hit a button then you shouldn't be surprised that no one wants to pay you very much. You also shouldn't be offended when your job is truthfully characterized as "just hitting a big red button in the morning".
My basis was that the button pusher was critical to your business and automation was not feasible, since you would have done that from the beginning. I don't know which economic concept this describes, but the idea is that you are compensating the button pusher based on their absolute, objective value (no pushing, no profit) rather than subjectively (skill-less "schlep").