As preface, I am an old school 1E grognard that still has not shaken those particular habits off of my current 5E games.
Cool, so your games are still awesome, then?
I also really like how 5E really has much in common with 1E, ease of character generation and a good system in general. I tried to get back into 3,5 earlier this year, but it was just a bit much to really DM.
3.5 was all about system-mastery, even for the DM, in self-defense (campaign-defense, I guess) and there was a lot of system to master.
Skipped over 4E since it was not D&D, only in name.
4e was remarkably different from all other editions, breaking with tradition and dropping sacred cows faster than BSE...
So with that said, as an old grog, I really do not like the way some races and classes are presented in D&D, thankfully I can nix certain races and classes without effecting the system in general. So here is a list of what I disallow in my campaigns and why:
Dragonborne- Really? A munchkin gamers wet dream race come true, and a DM's nightmare on how to handle such a race in their campaigns. These are monsters after all, not heroic core race types.
Tiefling- Gee, really? really? Why on gawds green earth would a demonic creature such as tiefling want to be among-st the prime plane rabble? Another Munchkin gamers dream race come true lol.
Well, the Dragonborn is just the bowdlerized/nerfed 3.x-half-dragon or Dragonlance Draconian, but with a decidedly 'heroic' (if it had been 3.x, their favored class would've been Paladin) backstory, and the Tieflling, likewise, toned down significantly from the planescape/3.x version, though sinister as ever.
Warlock- OMG shades of WoW lol! I nixed this class right off the bat, pacts just do not jive with my campaigns personally and seems better suited as a class for villainous NPC's.
Sounds like mostly a flavor issue, and it's been with the class since it's inception in 3.5, Complete Arcane.
At least any actual satanists wanting to play 'that satanic game, D&D' might be less disappointed than they would've been in 1985, when they find that the Warlock is now available... ;P
Paladin- I did not nix this class but went old school. The artwork in the PHB for the pally is so wrong on so many levels lol. So what I did do with this class was just make it for Humans only, Lawfull Good and Oathbreakers are N/A.
That'd be a quick old-school-flavor fix, yeah.
As I said upstream, 5E is probably the best version of D&D I have played
Well you
did say you skipped 4e, and aren't up to the challenge of 3.5/PF...
... so, excluding those two, sure, easy call.

I think 3.5/PF, though in a very different - player-entitled, rather than DM-Empowering - way, may be too close to call.
, not too complicated, not too simple, it hits that sweet spot for RPG's just right.
Once you cut all that 21st century crap out of it, anyway. ;> And, y'know, RPGs really are /very/ complex, and usually even more complicated than they are complex, anyway. 'Too simple' too easily shades over into 'not an RPG...'
No need to insult me with a troll label just because I do not like Dragonborne or Tieflings in my campaign.
No need for you to insult people who play them with the 'munchkin' label. See how that works?
I kinda wish WotC would have just put a supplement out with monsters as PC's
Volos, came out pretty recently with a number of traditionally-monstrous races...
instead of carrying over old 4E races.
The Tiefling was introduced in planescape and playable in 3.x, half-dragons 3.x, draconians back to Dragonlance. So, 'old,' yes, 4e, not so much. That said, I agree they could've waited for a supplement like Volos, and Warforged for an Ebberon book.
As for why Pally's are Human only, being old school AD&D grog, thats just the way I feel.
And that's all the reason we need!
In most fantasy literature and legends represent Paladins as human IE Charlamain, King Arthur, Sir Lancelot and so on. Not angry looking orcs. (another residual from either 3E or 4E).
The iconic 3.x Paladin was Alhandra, she was human. The full-page Paladin illo in the 4e PH was of a half-elf, but the stereotypical race for it was Dragonborn, typically worshiping Bahamut.
The half-orc paladin was a notorious 'against type' build you saw in 3.x & (once half-orcs became available) 4e, I suppose, though it should have been getting a little tired by then.
FWIW.
What Races (classes) do you allow or disallow in your campaign?
Typically when I run 5e, it's a 1st level introductory game at a convention, hoping to introduce the game to some new players. For those, I use the optoins in the basic pdf, so that cuts all but 4 classes and uses only one sub-class each. Slashes D&D right down to its essence. Likewise, no funky races, no variant humans. KISS.
Obviously, when I run AL, it's the virtually-anything-goes AL guidelines. Meh. Tolerable for the most part.
Once I wrap the pre-5e campaign I'm currently finishing out (campaigns take a while in a 2-hr weekly time slot!), I'll most likely start a 5e campaign. I'm already mulling over the character creation, and it will definitely be restricted, because it's a focused campaign concept. It's not just a matter of cutting classes and races, but of limiting the number of PCs (typically to 1) for many choices. So no two PCs can be the same sub-class, no two can be the same non-human race ('cept halfing & variant human, but they're limited, as well), and no more than half can be human.
Yeah, variety.
I'm also toying with a last-ed Gamma World variation on random stat generation - your choice of class determines one high stat, your choice of race the other - the rest are 3d6,
in order...