Tony Vargas
Legend
The point's already been raised that most non-casting, capable warriors in genre are usually very capable in quite a few other areas - not just athletics & intimidate, but being downright acrobatic, being educated (for the setting), stealthy, able to make and repair things, track, survive in the wilderness, etc, etc, etc - often all I one character.Yeah, there's no need to put all that in a fighter class because it's already there in other places. Backgrounds, skills, ability checks, etc. It's also in the name: "fighter". Seems odd to me that someone would choose a "fighter" class and want it to add more to the other two pillars more than the....er...."fighting" pillar.
In 3.x, you could do a fighter/ranger/rogue and come up with a fair approximation, though your BAB suffered slightly, your skill lagged real rangers & rogues, and, that 4th level of ranger could mess you up...
In 5e Backgrounds are clearly a step in the right direction, just not a large enough step.
The balancing of classes within and across pillars is also questionable. A prepped caster like a wizard, cleric or druid, can change out his spells to be able to handle each pillar exhaustively, or choose a balance among them and make the determination of where to focus dynamically by choosing how to expend slots. In stark contrast, less flexible casters can only make the latter sort of adjustment, and non-casters are hard-coded to whatever balance of combat, interaction, & exploration abilities their class & background give them.
Hypothetically, imagine a class that has the Champion's combat ability and the Thief's non-combat ability? Would it really be at all 'broken? If you didn't have the poor fighter & rogue to compare it to, I mean. Compared, say, to the bard, cleric or druid? Would it dominate play?
I think the only possible answer is: No. It might offend any number of philosophies of class design, and enrage fans of traditional fighters and thieves by being strictly superior to their favorite classes, but it wouldn't exactly break the game. Heck, it'd barely climb to Tier 3.