Sounds reasonable.
> But let's not do it just because we can imagine something.
Does this mean I need to take down that ad on Craigslist?
As long as the cafe pays taxes, follows the law like any other business, and claims you as an employee, sounds like work to me.
You could also be part of a nonprofit that holds mini-concerts in nursing homes, provided that all the appropriate tax paperwork gets filed.
Would self-employed work not count under your system? What if I was doing something with the hope that it will make money in future? What if it's not, in fact, intended to make money at all, but would be non-profit work? If I set up a company that would sign off on me and my friends, would that change anything?
Managing a cafe in Cafe Simulator 3000 because you want entertainment: not work (but these games often do a good job emulating the monotony of work in the long run).
The lines get blurry when you're managing an actual cafe because you're bored and want entertainment.
Hanging around a cafe because your friend works there: not work, even though some people sometimes pay other people just to hang around in a cafe.
This is very far-reaching. We might also imagine, that, if only we sacrificed any and all redheads once they reach the age of eight to the volcano god, the world would be blessed by everlasting peace, wealth and bliss. But let's not do it just because we can imagine something.
> suggesting that what many of these people do is in fact unpaid work
No, it's really not. They accidentally do something that other people in other contexts will pay others for. It's not that you'd have to pay someone to play video games with you if some stoner wasn't online. You'd play video games with ... all the other people who want to play video games.