Seems rather odd that your desire for simplicity begins and ends with the guy who's approach to combat is fighting like your usual fantasy hero, without spells and magic.
There is some degree of sense to making the most common sort of fantasy character the simplest, it'll mean more people can play it. There's also a degree of sense to making it over-powered - more people would want to play it.

Then there's a degree of sense to making it under-powered - lots of people playing it will be less disruptive. Then there's also a degree of sense to it being perennially broken - lots of people play it, so that popularity must meant it's 'fine' as-is.
;P
Because my character concept in a social game might involve being an aristocratic warrior that doesn't have supernatural powers? Actually, in 3e I would have selected a Swashbuckler or Swordsage and in 4e, I would have definitely gone with a Warlord.
Sure. Those should be perfectly valid. It should also be reasonable, in such a campaign, to have a non-warrior, with no particular combat prowess either martial or supernatural ... (Something D&D doesn't readily do).
But can you not see the issue with that statement? It's like saying, "Well if you're playing in a combat heavy game, then you shouldn't choose >insert other class here<." D&D has been moving away from that kind of thinking for a while in regards to the other classes.
What other class would you insert? No 5e class is actually /bad/ at combat, once you factor in using combat cantrips & spells.
My games involve more social and exploration- even in 4e where everything was supposedly about combat...
Oh, sure, that's why it had those big ol' 'Skill Challenges,' to focus more on cobmat ... and why 5e got rid of them, to focus less on combat... ;|
and I expect classes to be serviceable in all of them. No individual character has to excel in all of them, but I expect basic character archetypes of warrior/rogue/priest/mage to be workable in all of them.
An individual character can certainly excel in all pillars. It might depend on preparing the right spells that morning...
I modified the Fighter (it had a host of other issues) in 3e and welcomed the introduction of the Swashbuckler and was even more excited about the Bo9S classes- WotC responding to people who thought lack of the option was a bad feature. I didn't mind the Fighter being so straightforward in 4e because it also introduced the Warlord to fill that archetype- and was introduced as WotC's response to people who felt the lack of the option was a bad feature.
5e has so far concentrated very heavily on accomplishing the feel of the classic game, so bringing in a 3e feel, let alone a hint of 4e, is incumbent upon the DM, and includes adding optional material, or outright creating it, yourself.
It makes some sense, from the point of view of consolidating brand identity. But, at some point, they really should bite the bullet and carry through on supporting '3e feel' better, and '4e feel,' at least a bit.
And that's just in D&D. When I get to play and run other games, you had better believe there are all kinds of non-magical warriors with varied and utilitarian abilities all over the place.
Sure, other systems don't have D&D's baggage.
It is my hope that- just like they did in previous editions- WotC will realize that it's a bad feature.
When a bad feature has been standard equipment for 40+ years, your customer base will have come to consist primarily of people who can stand it being bad, and people who won't stand for any attempt to fix it. Any alternative feature will have to be after-market and marketed... carefully.