I think I agree with everything you've said here, but I want to offer a caution to those who pursue hard work that is fun.
I've worked in all permutations of your descriptions. If I believe in a project and can get good results on it, and much moreso if I'm having fun, I will work very hard. If I don't believe in it or have trouble getting good results or no one cares, then it's very hard for me to motivate myself.
Obviously, I prefer the situations where I'm highly motivated, and in fact I've worked very hard on some projects. Too hard, in fact.
The fact that a project is something you believe in, that you're highly motivated, that you can make a difference with it, or that you're having a lot of fun, doesn't make overwork healthy.
I've overworked myself a couple of times in my life. I hesitate to describe the worst case; I don't think readers will believe my description of what I did. Suffice to say that I worked on a new system project at Apple and was highly motivated to make it succeed (it didn't). I owned a small non-tech business at the same time.
I worked way too hard for a while. I didn't mind it. On the contrary, I was deliriously happy to do it. Nobody had to ask me to work hard. But it still did me harm.
I don't know for sure that working like that caused or contributed to the chronic illnesses I now have, but I do know that the literature on one of them says that it's correlated with excessive hours worked and excessive exercise. I did both. (My side business involved a lot of intense exercise.)
Oh, and if the overwork did cause or contribute to my chronic illness, then it may also have cost me a fortune. I went bankrupt in the process of getting one of those illnesses properly diagnosed and treated. So even if hard work does happen to pay really well, that doesn't necessarily make it worthwhile--not even necessarily financially worthwhile.
Again, nobody made me work like that. I did it because I was motivated and having fun. It was nevertheless very bad for me. That became clear over the months after I did it, and I may still be paying for it.
You might think that I would have learned my lesson from that episode, and that's true to some extent. I've never worked that hard again. I have worked too hard since then, though. It's a consequence of personality traits, I think. It's a trap I can too easily fall into, even though I know better. So I have to keep watch and listen to my loved ones and my doctors when they warn me that I'm trending that way.
In short: don't think that fun and motivation make you immune to the ill effects of overwork. They don't.