Starting as a Super Mutant though, demands a completely different situation. I don't think anyone has the patience for multiple races for starting out. What are we going to do, a Broken Hills-esque starting place? Humans and muties in harmony? Please.
This is where I'd see the problem in having this as an optional part of the game (and why I think the idea of playing as a Supermutant/ Ghoul would work better as a spin-off game than a part of the main series.) We'd be talking about likely having to come up with a separate original story for each race, and then still working it out so they all end up on the same path regardless of race. In order to be somewhat believable, it seems to me you'd almost have to work out a dialogue set for each race you could be for everyone you encounter. (Because what's the point in even playing as a Supermutant if only the major NPCs even make any comment about you at all, and then only in the first line or two - after which it all ends up the same again?)
I mean, it could be done in the same way that nothing is impossible and I'm sure if you really wanted to work something like this into a non-linear and free-form curren-gen open-world roleplaying game (which already has some problems doing all of those things as well as it arguably should) then it's at least possible in theory.
But I think you'd be better off working out a storyline for a spin-off Fallout game with the express purpose of exploring what it's like to be a protagonist dealing with being a Supermutant. And then possibly another line dealing with being a Ghoul. It just seems easier to me (and more likely to succeed, as well) to make a game with that as the central focus, as opposed to giving the player more choices - which would likely result in those choices being much shallower than they could be.