One issue with the current model is that Frank has to retire in due time. He cannot be allowed to work for cheaper while receiving benefits, otherwise he's taking the spot of younger folks who are supposed to be working there at a normal wage and finance his benefits.
You misread the conclusion. There is no need to bring down the minimum wage for everyone, just because he doesn't need a full wage. He can simply work part time and get half the money.
I gave two examples where increasing the hourly rate would make it so that the business would not hire the worker because it would provide negative value to the company.
Working half the hours does change the fact that each hour loses money for the company.