Can someone shoot film and actually work full-time as a photographer?
I don't know any more than he does! But let's think about it a little, shall we?
Daniel notes that speed is of the essence, in many cases. So, eliminate those, obviously. You don't have to get too crazy, the turnaround on film isn't that terrible, but for stuff like spot news, film is probably out.
Assume that the target is digital, at some point. If it's going online, or into print, it's going to be digital eventually. The only place it's not is in fine art prints done in a darkroom, I think. Maybe there are a few shops still halftoning from slides, but I doubt it. So your product is getting scanned at some point.
Eliminate anything about the "distinctive look of film", then. If it's going digital eventually, it can be shot digitally and processed to match whatever look you want, including film looks (this is demonstrably true, I am starting to look around more closely and I suspect that quite a lot of the "film" we see online is in fact faked by people who are not as good at faking it as I am -- and I'm not that good.) This is probably true for fine art prints and other "pure analog" processes too, but we've already ditched those.
The reason, therefore, you're shooting film is because of the way it forces you, the photographer, to work. You might as well scan the negatives, then. Well, there's one corner case, I guess, where your process extends to prints which are then scanned. Call that an outlier. Maybe we'll look at it later.
The basic process, though, is going to be to shoot film, develop it, and scan negatives.
What is the downside here, for the client? Fewer frames to choose from, and a slightly slower turnaround. A few hours longer, which I cannot imagine is a deal killer for most work. If you're printing prints and scanning those, the turnaround goes up another hour or two. So what? Anyways, we're eliminated the small family of "speed is everything" gigs already. We're only looking at work where you can afford a day.
I think the elephant has to be the number of frames to choose from. Clients more or less have to be uncomfortable with the idea that they're not going to get the shot they need, if some jamoke is shooting film. If said jamoke is printing prints and scanning those, there will be even fewer shots to pick from because the jamoke ain't going to print every frame.
The trouble is, then, that the client doesn't want to the photographer to be a photo editor. Or, more exactly, shooting film is only going to work if you can gobble up the role of photo editor. The contract has to be to provide final pictures, or a very small set of final candidates to choose from. In these scenarios, the film delays become irrelevant. You're swapping photoshop time for developing time. If you're shooting film, you're being careful up front and doing less 'shopping in post, because, film. You're using a good make up artist instead of pissing away time on "frequency separation skin work" later, and so on.
Coincidentally, this is exactly how wedding photography works, which is why people can get away with shooting weddings on film.
So the trouble is, I think, really that the photographer isn't supposed to be doing the photo editing job as well in many cases. Photographers are expected to shoot a pile of frames, and then work with the client to select a broad sheaf of "possibles", then go back and retouch those, and finally help select finals out of that lot. The collaboration is supposed to take place "in post" rather than mid-shoot.
So, anyone shooting film has to be offering a kind of soup-to-nuts package, in which the client is more or less hands-off for a large part of the process. Big meeting up front to hammer out the requirements in detail, shot lists, whatever, then the client goes away. Big meeting at the end to pick out the finals out of the small collection of candidates.
What clients want to work that way these days?