They just wanted to be weird no matter what. For them, I think variety is important and trying to reign them in actually ruins their fun.
In a campaign that seeks consistency but wants to allow for full player choice, the setting could have a mutagen backstory (aberration magic, Far Realm virus, divine curse, etc.) to cover these unique individuals.
For most players, though, I think races are primarily a vehicle to confer a bundle of powers on the character. That's actually a useful thing in my opinion--powers have to come from somewhere and having them come from race lets us un-frontload classes and allow greater diversity and customization. If that's the role, though, then the narrative stuff (description, culture, how they act, etc) actually becomes an unnecessary complication on the bundle of powers. If I want +2 dex and you're telling me that in order to get it I have to be "fanciful and not serious" then we have an issue if I don't want to RP that. It is an unnecessary conflict.
In the second scenario, we'd be better off decoupling the bundle of powers from the narrative aspects of race and just create templates or something (i.e. military upbringing, streetrat, etc). Then people are free to be a member of whatever race they desire and take on whatever role they desire without having to compromise on how they perform in other situations. Converting most races into background templates would be as easy as changing the name (with a few outliers due to size, innate magic, etc).
I agree, but I think there is another nuance there.
If there are 3 physical stereotypes -- thin & agile, standard variation, or short & stout -- and 3 cultural concepts -- fey/forest affinity, versatile, or earth affinity -- then the race of elf, human, and dwarf is a combo of each. That is, you don't get the complete elf racial mechanics when you strip out the cultural/environmental role, you only get something like +2 Dex leftover.
If I was to reskin an elf as a human, I could make it a tribe of fey-touched forest-dwelling humans, in order to lock in the racial aspect with the physical stereotype.
If you disconnect the physical stereotype from the racial concept, then you're implying that non-human races have the same body diversity as humans. You can have obese elves and tall foppish dwarves.
Which is fine, except that some of these racial physical stereotypes is an easy (maybe lazy) way of classifying their non-humanity. Remove some of those stereotyped traits and the racial lines are more blurry. The obese elves in the forest and the tall dwarves living on the mountain start to feel more like eccentric human colonies.
So then you really have to try hard to make the non-humans think and behave differently than humans -- otherwise they're just regular people in funny suits that are now less funny-looking and more ordinary, so might as well take off the funny suit and call yourself what you are: a human variant.
But in tackling such fictional issues, D&D isn't exactly well-known for taking the deep-thinking route.