IME most players fall in love with a particular concept but actually never roleplay that concept. I have been playing since AD&D first came out and it is unusual to see someone actually RP their character. This is one of the reasons I don't see the need for a bunch of races. Most people cannot even RP a human that has a slightly different viewpoint than themselves much less a different race. Most of the time they come across as simple charactertures.
I believe in part it is because of the kitchen sink approach of D&D. In the '90s I had a group playing version 3. All of them came up with "cool" character concepts, but none of them actually played even their alignment much less their "cool" idea.
That same group playing Vampire the Masquerade was exactly the opposite. Every player dropped deep into their role and had unusual and interesting interactions.
I observed the same thing with a different group playing Shadowrun vs. D&D.
On the other hand, in Champions all the players did was focus upon how "cool" their power concept was and did little roleplaying.
I have also observed that the same players that always want to play a new race have some combat power idea in mind. However, it rarely works out because a good DM challenges the players on a variety of fronts so that one-trick pony becomes boring to play. So instead they roll up a different character with a different race with the same personality and a different "trick".
These same players also tend to choose names for their characters which clash with the setting -- character names that fit better in a Monty Python skit.
I am not saying this applies to all groups. I am sure others have had different experiences. Mine come from playing and running a games for almost 40 years. I have played with at least 20 different groups not counting conventions and observed many more. I am also not saying one way is better than the other -- whatever makes the game fun for the whole group.
Limiting what races you allow in your game might also make it easier to find players who are more compatible with each other. Those that hate it will move on and those that can create interesting characters with even a single race choice will stay.