One thing I wish that 5e had done was make explicit what the tiers of play actually mean. If I'm an archetype of my class, what does that actually mean? Is an 18th level fighter still bound by normal human standards or not? I'm very much in the "no" camp, but, I do wish they'd actually step up and make it explicit.
I think its a matter of degrees for most people.
For example, I think most people are okay with a 20th level fighter being stronger than the strongest real life person. But how much is the question? 10%, 20%? Maybe. 100%....probably not.
Same with speed. Could the fastest 20th level fighter keep up with a greyhound dog? Yeah I could see that. A cheetah? Probably not.
Then again...I think there is some power level where you have to let all characters break the mundane limit, or balance is beyond impossible. Maybe that is "epic level", maybe that is the 16-20th level tier, but I think it has to be somewhere. And some point "Joe the Fighter" gains a little immortals blood, becomes the chosen of a god, absorbs some of that magic from those items he has had all of these years, etc.