This analysis totally ignores a whole bunch of factors, including that you can’t pay someone else minimum wage for a bunch of things, and that “hiring someone to do X” has a huge transaction cost associated with it. Not just the hiring part, but the coordination, etc.

The “can’t work more hours” piece actually works towards your argument for finite time: why would you want to spend any of your outside-of-salary time doing stuff you don’t want to do that could pay someone less to do?