Not all issues of color pie balance have strictly to do with mechanics. Some of them are more flavorful: For example, almost every color has a "characteristic tribe" that its small creatures default to in flavor-neutral settings, that are a recognizable type of fantasy creature, and that exemplify the color's philosophies. Blue has Merfolk, black has Zombies (and Vampires, from time to time), red has Goblins, green has Elves, and white... well, white is rather deprived on this front, though it may get lots and lots of different variations on sentient animal people and clannish groups of sort-of-normal-people-but-not (see Kor and Kithkin). Currently the white characteristic race is "sort of" Humans, but there are plenty of those in every color, so it doesn't feel right to really have that type in this position.
As this is both a design and creative question, both Doug Beyer and Mark Rosewater are qualified to talk about it, and they recently have on their respective Tumblr blogs.
When howler13 asked Beyer, "A topic that comes up on Maro's tumblr from time to time is white's characteristic race. Currently he says that Humans are it but that design is in search of a different one, since Humans are in all colors. What are your thoughts on the subject?" he replied:
I agree that Human isn’t a great answer for white, because we like to put humans in all colors. It’d be nice to have a staple race that says “this expresses white” just by being that race, and to break up all the human-ness.
Unlike iconic races, though, I think it’s fine for each color to have a small cluster of small humanoid races that it rotates through as we move from setting to setting. Certainly some races are more common for certain colors (e.g. Goblin for red), but it’s fine for those races to go away for a while, as long as there are cool other species that can occupy the same niche (e.g. Satyr or Devil).
White has had leonin, kor, and kithkin, which can all work depending on the setting — but we just find that many settings don’t want any of those. Dwarves may be the right answer for white someday, or something else we haven’t thought of yet.
In the comments, yewlas noted, "The problem is that those races at common ought to be resonant and recognizable to people not familiar with the game or just starting. Most people could tell you what a goblin or elf or zombie is like," a criteria which Dwarves definitely fit. Meanwhile, the-machine-orthodoxy said, "Dwarves fit so nicely. They care about order, tradition, and law. Sure, they may traditionally live in Mountains, not Plains, but I don’t imagine many Vampires prefer the swamp over a good city."
When manacharged asked Rosewater, "Some people think dwarves could be white. Do you see it, or do you think they are too-mountain centric?" he effectively gave the go-ahead, replying,
I think there is a version of dwarves that could be monowhite.
So there we have it. Tolkienesque Dwarves - perhaps with the carousing and material wealth obsession aspects turned down, but definitely with the orderly engineering, martial honor, courage, and respect for tradition turned up, are possibly the strongest candidates for a white characteristic race. It is, for their part, not hard to see them in a core set, and they are the only majorly used fantasy literature race that is conspicuously absent from the present Magic milieu with the return of Orcs in the upcoming block.