My group doesn't typically choose "unusual" races, and we don't tend to got through characters, but here are my thoughts on the matter.
IMHO, setting limits on character races matters most at the beginning of the campaign - that's when the majority of the characters to be used in the campaign will be generated (barring a TPK, of course). After that, it will usually only be the occasional unraisable death, or new player, that will require introducing new characters.
Additionally, for later characters, (except for with new players) the players will have a better idea of how the game works and what roles different races have in it. As such, they are more likely to choose something that fits in the campaign, and be aware of the RP consequences of choosing something that doesn't. For example, if the PCs in game are involved in a group of minotaurs wiping out villages and eating everyone inside, a PC who later plays a minotaur ought to know the RP consequences of doing so.
That's something I've learned from an experience with my friend as a DM - he made RP consequences for playing certain races, then DIDN'T TELL US. Another friend, who played a dwarf, was quite unhappy about all the prejudice he faced in game (the dwarves are the "evil empire" in game). In that game, I play a drow - though in that they are a desert dwelling empire who think the sun god is evil, which causes problems with the other peoples who have the sun god as the top of their pantheon.
My campaign I started when only PH1 was out. Races were all PH1 player races, plus kobolds, and no tiefling (tiefling were to appear "in game" as a new race - in fact, the eladrin paladin got changed into a tiefling by standing too long in energies spilling from the demon rhelm into the "real world"). Elf and Eladrin are the same "race", just with Eladrin being the "flying castle" elves, and Elfs being the forest elves.
Now, as things stand, the other races simply don't matter - I don't have to worry about them until for some reason a new character is needed. So, if Genasi don't fit into my world... who cares? That said, this is how I would treat the races:
- Would never have been a problem: gnomes (forest halflings), deva, half-orc (very rare, but exist), warforged (dwarf-made war machine), any goblinoid (majority race in the setting),
- Would be okay now (my campaign setting has progressed, openning up plot reasons for new races): drow, shifters, goliaths, wilden, changelings, minotaurs.
- Might be okay in future (when the PCs get to upper paragon/epic, further room opens up for wierd stuff): gitz (both types), shard minds, genasi.
Personally, I don't get a lot of the sentiment "I don't like race X, they don't work in my campaign." Perhaps they don't... but so what? After the campaign has started, does it really matter? The times when one needs to worry about new races is quite rare, and by then the PCs should have a better idea of how things work. And personally, I don't mind a PC being one-of-a-kind - they are PCs, after all, and there is no reason why they can't be the D&D equivalent of the black guy in medieval england.