Sure, retirement and those other kinds of work you mention aren't incompatible. I think when we talk about retirement and not "working", we're specifically talking about not having a job that pays money. Though many people still consider themselves retired while holding a part-time job or working freelance some number of hours.
This is why in part I think the distinction between "FI" and "RE" is pretty small. I absolutely agree with you that the important part is financial independence, getting to a point where if you quit or lost your job tomorrow, and never brought in any labor-related income again, you'd be fine. From there it's just defining what life means to you. You might stick with a 9-to-5 for a while because that makes you happy. You might drop to part-time. You might quit entirely and focus on personal projects and interests (like the hobbies you mention). Or you might take 5 years to focus on personal projects, but then take a full-time job for a couple years just because you feel like it, with the knowledge that you can quit at any time if you don't like it.
> I would definitely challenge from a general standpoint any life where you’re not doing something productive.
Eh... if someone decided to retire and spend every day of the rest of their life going to the beach and lying in the sun, that's... fine? It's not what I'd do with my retirement, but I don't think I'm qualified to tell someone else what to do with their life, especially if they're financially independent and aren't a drag on anyone else.
But yeah, for me, I do agree that I want to be productive to some extent. But I love the idea of even that being infinitely flexible. Right now if I don't feel like being productive I can dick around on HN for a little while (like I am right now), but I have to limit myself, and get back to work soon, hoping that my short break will help me gain some desire to be productive. My midafternoon time is not my own; to a very real extent it belongs to my employer. I feel guilty about not being able to focus on work right now, and I hate that feeling. If it were just me doing whatever I want to do, I might feel guilty about not finishing a fun woodworking project, but that guilt would be isolated to myself: I'm not depriving someone else (like an employer) of something they're entitled to.
And with that... back to work.