Tony Vargas
Legend
That could cover a big chunk of it, depending on how far it was taken.So apart from The Class That Shall Not Be Named
What have we got, just in gamist terms? Tanky DPR (Champion, BM, Berserker - pretty thoroughly explored, really, with more in SCAG) and sneaky DPR (Thief, Assassin). Apart from the very broad 'support' category, for obvious reasons, what does that leave? Battlefield control, blasting, lockdown, mobility, utility in the other two pillars... versatility to cover several of those? And using what mechanics? Extra Attack, CS dice & a dozen or so maneuvers, Rage, Action Surge, Expertise...what else is missing in the non-magical realm?
Seems like there's lots of party-contribution and mechanical design space.
Most concepts get a smattering of nominal coverage already, though, mostly through minimal-mechanical-impact Backgrounds. In the same way you could have asked 'wouldn't that just be a Magic-user?' of any Sorcerer or Warlock or Bard or psionic concept, had they not already been broken out along with the Wizard, it's tempting to look at a class as generic-sounding as the Fighter and assume anyone who, well, fights, can be wedged into it, somehow, and that anything it doesn't already do must not be possible.
A non-magical crafter (but exceptional enough to be a real asset to his allies) would probably fit neatly as a sub-class of Artificer, if Artificer rated a whole class rather than being a sub-class, itself. I guess you could turn it around, and have a Sage class that has a nominally-non-magical Alchemist sub class, an overtly magical Artificer, and a non-magical gadgeteer, along with a Lore sub-class that knows stuff more than makes stuff.I can think of subclasses, but not a full class ... well, maybe a gadgeteer?