Infinite possibilities. Never how I thought of it before, but I like it. It's the infinite possibilities that make this game so great. And no, I'm not talking strictly about races and classes as the OP is, though I'll get to that, I mean the infinite possibilities and diversity just in one gaming table to the next.
My game is different than your game, which is different from the next persons, whose is different from the next persons... ad infinitum! That's pretty f-ing cool in my opinion. We can all start out with the same building blocks, but what we construct in the end is all out own. Good stuff.
And yeah, that includes things like races and classes. My sweet spot is the kitchen sink. I like giving my players options, all the options. Core books, UA material, and even third party stuff as long as I get to look it over first and make sure it's not too wonky. If a player has an idea and it's a race or a class not already in "my" world... I add it. I've never found it too hard to find space for anything. More specifically, forget about it being "hard", it just doesn't phase me. I think of my campaign worlds less as "mine" more as "ours".
I swear I'm not some rainbows and sunshine hippy dippy whackadoo. I just not bothered by it. I don't carry my own personal biases into the game and I certainly don't care about how things "used to be". Don't care how things were an edition ago or three editions ago. If I want to play those games... there right over there on my bookshelf. That said, I've never gone back to playing a previous edition of the game, I always play what's current. Even so, if the mood struck me, the books are there waiting... watching... er, no, just waiting.
Now, every now and again I do get a hankering for something heavily thematic. Like say, an all dwarf party because the campaign is all about a dwarven mining expedition. Or maybe a party of all Paladins and Clerics, characters on some holy crusade. You get the idea. Either way I do find that when I restrict things like this the campaigns tend to be shorter, but all the same I'll run them when I get a nifty idea.
Additionally, if I'm running a published campaign setting, I will run it more or less "by the book". Which is to say if the setting comes with it's own set of restrictions, I'm probably going to adhere to them. These are cases similar to my "themed" campaigns in that if I really want to run Dark Sun, I'll run it by my players, make the settings themes and restrictions clear, and if I get the thumbs up we'll move forward.
Anyway, all of that said, and it's far more than I intended, I'm all for other folks running their games their way. That's the real infinite diversity I was on about to begin with. People don't need to like or agree with how I run my games, and that's cool. I've read enough posts around here by now to know there's some posters who run games I'd never sit down to, that's cool too.
Anyway, I think my point was something like... whatever floats your boat man.