I would say that 1e and 2e were also "Needless Complexity Editions", so really, it's a tradition...
Sure, though I feel like both of them largely-accidentally managed to use exception-based design to minimize the total amount of rules you had to either know or look up to a far lower amount than 3.XE/PF1. 4E also used exception-based design better and more consciously than 3.XE. One major issue 3.XE had was the "a rule for everything" approach, which no previous or later edition has really had, and loads of Feats existed solely to mitigate penalties to doing some manuever or whatever which only had penalties on it to justify a Feat existing. That's some real hardcore needless complexity.
This is every non-Original books or Basic edition of the game prior to 5e, really.
No way does 5E escape. 5E has less needless complexity, but it still manages to get it in with stuff like Hit Dice and Short Rest/Long Rest and so on. 4E also had less needless complexity than 3.XE, though uh, it still had it, thanks to the appalling action economy.
Wasn't all exercise basically naked exercise back then?
Apparently not, though the Greeks sure loved to strip off and start running or wrasslin' or whatever.
A film of one guy, running alone, doesn't indicate much.
Take two people. Have them both run unarmored - show they are about the same speed.
Put one in armor. Have them race the other unarmored. See what happens, and you may have a point.
It's not "one guy", though, experimental re-enactors (many of whom are also historians or archaeologists) have been doing this for decades. Mike Loades, I think it was, though don't quote me on that, even rode 250 miles on horseback in full plate to see if that was doable, and it totally was (I mean, riding 250 miles is never fun-fun, but he was in no way injured or incapacitated or so debilitated he couldn't act normally or anything). But if you have questions, just check out YouTube - there's loads of people doing fancy stuff in plate.
Would someone not in armour at all run faster? Sure, probably. It's 50-70lbs of weight, however well-distributed.
Would someone in virtually any armour at all run faster though? Hmmmmm much more questionable.
Would someone in a chainmail hauberk etc? Almost certainly they would not run as fast as the guy in full plate. A guy in crusader-era chainmail pajamas would be even slower.
Would an adventurer with say, a 50lb backpack? He'd be probably be slower than the guy in 70lbs of plate (unless, perhaps, he lived for "leg day" and was running in a very straight line).
I can't accept that the answer to having a problem with a game's verisimilitude is, "don't worry about it".
I mean, this is definitely not the worst "realism" or "verisimilitude" break D&D has, not by a long shot (falling is far worse, for example, as is the total lack of rules for a lot of stuff), so you actually "not worrying about it" with a bunch of stuff if you're playing D&D and you have like, less than 20 pages of house rules. Sheesh, D&D's weapons alone are probably drastically worse for both realism and verisimilitude (what genre/sub-genre do you refer to re: verisimilitude btw?) than its armour. D&D's weapons are a giant disaster re: both.