@Stormonu Well said. It's honestly surprising how many folks respond to this with either a blatant slippery-slope argument, or a really strange false dichotomy argument. A little creativity--indeed, a little bit of
Gygaxian thinking, dare I say--is more than enough to preserve the traditionalist purity many DMs seek.
While I see what you're getting at here and to some extent agree, the inherent risk is that you'll run aground* on table mechanics: "Hey, she's got one of those to play, I want one too!", meaning that thing that until a moment ago was a complete one-off either a) suddenly has to be duplicated or b) is liable to cause resentment at the table.
Don't see how you couldn't run that with the same thing? Two people want to play minotaurs. Boom, a brother and sister (or some other familial, platonic, romantic, economic, military/political, or religious relationship) who were cursed for stealing from the Temple of the Sacred Bull, or who pissed off a witch, or who were afflicted from birth with a strange curse, or...
I mean, after all, the
literal mythical Minotaur of Greek myth was a one-off creature himself, as indeed were the vast majority of interesting not-fully-human creatures of myth.
More broadly, I also very much want to avoid the end-result effect where an adventuring party resembles the Star Wars cantina on feet.
People often use this as a disparagement. I don't understand why. Adventurers are already weird, likely to be subject to strange curses (or blessings...or both), consorting with dangerous or capricious powers, delving into knowledge and locations Man Was Not Meant To Know, wearing bits of bling stolen from dead people or recovered from seven different ancient cultures without a care in the world about fashion, etc.
Besides...do you
really have literally all five/six/whatever (I believe you've said you tend to have larger groups?) players insisting on playing races of such dramatic physiological differences? Even if you don't, are you actually avoiding the "cantina effect" anyway? For goodness' sake, if you have a human, a dwarf, an elf, a halfling, and a half-orc--all races with extremely long pedigree and well-established long before things like tieflings or (heaven forbid)
dragonborn--you ALREADY have "the Star Wars cantina on feet." You have inhuman colors (especially if that elf is a drow), inhuman sizes, probably obvious tusks and other non-human facial features (pointed ears, for example, are commonly assigned to
all of those non-human races), a high probability of significantly divergent build or muscle mass (indeed,
all of these races are held to have noticeably distinct silhouettes from the typical range of human shapes, except
maybe elf and half-orc).
Like...even if you literally restrict things to just the "core four" races, you already kinda have this effect
unless your players agree to mostly play humans. Which...if you already have that agreement, I don't see how letting one or two people deviate from it changes anything.
Which is what ties into the comments I made above. On the one hand, you could be presenting a slippery-slope argument: "if I let
one player have
anything Exotic™, then soon
every player will have a psychic flumph half-dragon from another reality and nothing will be special anymore." This suffers from the exact problems that any slippery-slope argument has, namely, that you haven't actually proved that this chain of events
must occur. Even if you have personally seen it occur in the past, you can
do something about it, it's absolutely not a guaranteed inevitable result no matter what you, the poor beleaguered DM who just wants a nice, normal, safe, traditional, unexceptional, ordinary, standardized campaign, could ever conceivably do.
On the other, you could be presenting a false dichotomy: "Either I let
everyone play
anything whatsoever, or I perfectly hard-restrict everyone to a single list of choices with zero exceptions." On this one, the very arguments used in favor of things like 5e (or old-school editions) take your argument down
for me. Isn't the whole point of "rulings not rules" and "DM calls the shots, the rules are always provisional" supposed to be that you not only can but
should make ad-hoc exceptions in order to "improve the game"? Why would player race choices be any different? Either make it a first-come, first-served sort of thing, or a lottery if several players want it, or (if you have a relatively high turnover of parties and/or PCs), have it go round-robin.
Heck, that last option even lets you
enhance the resistance to your dreaded "Star Wars cantina on feet" problem:
One, and only one, player gets to play an "exotic" race at any given time...and a single player cannot play an "exotic" race again until
everyone has gotten to play one, and "exotic" races can't be resurrected. If you lose the character, it's gone forever, and then the next person on the round robin has the opportunity to play something "exotic" if they like. Or, alternatively, to prevent perverse incentives to seek death when one's opportunity is up, the remaining players who want to play something "exotic" get the opportunity to
roll to see if they can make a new character with an "exotic" race, e.g. those who want to play one and haven't gotten to yet this time around roll a d6 every time their character dies, and on a 6, they can create an "exotic" race character. Now you have a fair system, with no perverse incentives to cause players to suicide a character just to play something fancy, and it not only naturally enforces a no-cantina rule, it even forces there to be
downtime between "exotic" party members so there's always some periods where all characters are so-called "normal."
* - I speak from experience here, and have had these discussions. Perhaps fortunately for me, the player of the one-off character was a real Leroy Jenkins type and ran it straight into its grave, whereupon the desirability of playing that species dropped considerably...
Don't see why you couldn't have a frank conversation with your players about it. "You can't because I want anything of this kind to be
actually rare and unusual. One of something is, literally, unique. Two of something implies too much. She asked first, so she gets to be a special thing. If it matters enough to you, you can request to be the one exceptional creature in the party next time." Or, as noted above, make a simple system to enforce the scarcity you desire. I didn't spend five minutes coming up with the above, I'm sure if it's not adequate for you then you could
easily come up with something better, seeing as you apparently have players very eager to play "exotic" races.
Further, you've made it pretty clear that you can set effective, well-communicated boundaries for your players. After the various conversations we've had over the years, you have never struck me as the type to get steamrolled by your players (or by
anybody, really). If they are so petty or so vengeful that "she got a special thing and I didn't" is enough to
actually cause serious friction in your group, I can't help but wonder how the group has managed to stay coherent for so long (or, if you regularly play with pick-up groups, I would have
serious doubts about whether that group will survive the first two months of play). And if they
aren't so petty or vengeful...maybe give them the benefit of the doubt? You may be surprised what a forthright, but respectful, adult conversation can achieve. And if it can't, well, again, not sure that group has a healthy dynamic.