In addition to my recent thoughts regarding the "PHB+1" policy and eliminating multiclassing, I find myself increasingly drawn to a position where the number of 'oddball' characters should be restricted. This is very much a matter of personal taste, of course, but I'm generally convinced that the game isn't actually helped if the party is made up of five characters who are each more specially special than the last. (And there's a reason that "Guardians of the Galaxy" introduces us first to Quill, the only human in that party, and why "The Lord of the Rings" introduces us to the hobbits first - in that story, it is the hobbits that are "us", with Aragorn and Boromir being super-humans.)
That being the case, I'm inclined to suggest that the party should contain no more than one member of an off-beat race, no more than one character with an off-beat class, and that those two should not be the same character. (Similarly, in Star Wars, you'd have no more than one alien, one droid, and one Jedi - with those three being different characters. Of course, that means there not being any alien Jedi in the game.)
There are a number of significant issues with this, of course. Firstly, what constitutes an 'oddball' race/class? Is it a non-human race? Anything outside of the PHB? Or something else? (My answer there would be "it depends". Gut feeling, especially since I'm keen to get away from the PHB races, would be non-human races and then non-PHB classes.)
Secondly, there's the question of whether the players would actually stand for that sort of meddling. As I've noted before, the GM gets to control everything else about the game - the setting, all the NPCs, and even the rules of the game itself. My position therefore is very strongly that when it comes to the PCs, aka the one thing the players get to control: hands off! This position, of course, very strongly contradicts that.
The third issue is probably the biggest, though: if the party gets to have one oddball race and one oddball class, who decides who gets that option? And surely, if two players each come with a burning desire to play a non-human PC, that's a recipe for at least one of them to be disappointed... perhaps even to the point of leaving, or even sabotaging the game.
The upshot of all this, after 400 words of waffle, is that I don't think this sort of a restriction is the way to go. Instead, I think a better approach is probably to limit just how oddball a single character can be (that is, you can take an oddball race or an oddball class), rather than limit the number of oddball characters in the party. Probably.