If you are going to use a Class-based system... then each class should have their own flavor and thematic intention story-wise.
In 5E in my opinion there are 3 Broad classes and 10 Narrow ones. Fighter, Rogue, and Sorcerer are the three Broad classes, in that their flavor and theming come out of their subclasses and not the base class. The words "Fighter", "Rogue", and "Sorcerer" are more catch-all terms used as a title heading to encompass all the different "real" thematic classes within them.
Whereas the Artificer, Barbarian, Bard, Cleric, Druid, Monk, Paladin, Ranger, Warlock, and Wizard all have their flavor and thematic intent baked into their base class, and the subclasses are merely different ways or paths to present it or to focus on a specific thing within the base class.
Having both types within the game is what causes all the hullabaloo, because two of the three Broad classes are the two purely MARTIAL classes in the game. Which means it gives the impression that the game is focused on magic because there's all these other spellcasting Classes in the game and only "two" Martial classes. But that's not really "true" per se... because all of what WOULD be the heaping amount of Martial classes are actually presented as subclasses under two Martial umbrellas. The Samurai, Thief, Scout, Assassin, Swashbuckler, Cavalier, Gunslinger, Banneret, Champion, Mastermind et. al... could ALL have been their own Classes in the game sitting right alongside the Cleric, Wizard, Warlock, Druid et. al. And if WotC had done that, there wouldn't be any of this caterwauling about not having enough Martial Classes.
Which is why I most certainly understand many people's desires for the condensing of Classes down to "Fighters, Rogues, Priests and Mages" or even "Fighters, Rogues, and Spellcasters" to make ALL the "Classes" be Broad. And then every "Subclass" or whatever designation you use becomes Narrow. It makes sense from a categorization perspective to do it that way. Make it so that none of the umbrella Classes have much flavor in and of themselves, where instead all of their unique story perspective and flavor comes from the subclass.
But I think the reasons WotC don't do that is because of tradition AND the fact that most of the Classes in the game have unique game mechanics to themselves. And as a lot of people want (ne DEMAND!) unique game mechanics for Classes (see the multitude of Psionics debates)... condensing Classes down into three or four Broad classes condenses the types of unique game mechanics you have for each of them (unless you start adding all kind of mechanics back in via Feats or somesuch.. but that'll piss off a bunch of people that way too.) So I suspect any sort of condensed mechanics or 'pick 'n choose' mechanics via Feats would be an anathema to a vast majority of the D&D populace.
At the end of the day, I personally would prefer Narrow classes, if for no other reason that it would force WotC to turn all the Fighter and Rogue subclasses into their own specific classes (like Pathfinder does for the most part)... thereby giving us a huge influx of Martial classes to add to the Caster ones... and thus finally ending the endless wall of complaints that WotC cares more about spellcasters than they do martial warriors.
