This is interesting to me, because I have never experienced anything of what you describe when working for somebody else. Maybe it's because I work in an office, and so there's a very clear change in environment that affects my ability to focus on different things: office=paid work, anywhere else=not paid work.

In any case, what you describe seems like a pretty big limitation to me. If your employer isn't asking you, or pressuring you, to do more work, then they really shouldn't be held responsible when you do. I wouldn't paint my neighbor's house without having been asked to and then be upset with them for not asking me to (and therefore not paying me to) paint their house. That's nonsensical, but it's also an analogy with limited applicability.