I have occasionally billed for time spent in the bathtub. I didn't go into the tub expecting to be paid for it, but once in a while I have a eureka moment, get out, write down a solution to a long standing/hard problem, bill a half hour for it, and go back to the tub.
It's rare, and I only bill it when it was genuinely valuable, but it's not totally out of the question!
This sounds like some kind of contracting relationship. I have a regular daytime job, but contract in my own time, and I find that that is a much better construction for me to weigh putting in more time, getting paid, versus taking my rest (or whatever you want to do when not working). That might not work as well for others, though. My day job, at fixed pay, excites me a lot, which is a reason to put in too much time. I have no over-demanding managers, forcing me to stay late, like others may have. So, here's at least three powers that may make someone stay late, each with its own countermeasures, all very dependent on that individual or their situation. I'll repeat them: excitement/involvement, money (hourly rates), and scare of being fired.
At the end of the day, it comes from one's own motivations and I do feel your sentiments regarding the 3 powers you mentioned.
1. Excitement/involvement is tough to manage but at the end of the day, if you're burned out, the excitement dies down. At least that's what happened to me. And as mentioned, there are times when I didn't think of how to solve a problem that the solution came to me.
2. I had to overcome the obstacle of money and the fear of being fired. In the past, it used to affect me greatly but I've learned how to deal with it over the years through chanting (meditation), philosophy and other activities.
I do all my best work in there and I can't even bill for it.