While I'm not an enormous fan of either dragonborn or tieflings, I think it was a good idea to include them in PHB as a 'core' race, even if they're not necessarily the most populous. It was really an act of mercy, for both players and DMs.
I used to help run a freeform play-by-post website, you see. And in our setting, dragons were rare and incredibly powerful beings, and demons and angels didn't even exist. Despite this, we'd still get at least one application a week from a new player trying to play a half-demon prince, or a human with a 'strange curse' that makes him look like a dragon.
The fact is, some people just really flipping love dragons and demons, and will do incredible backflips to play them or something like them. Also, I play with a lot of really casual players, and there's something about the tiefling and dragonborn that really trips their triggers. "I can be a half-dragon? I can be a freaking devil! Awesome!"
New races seem to follow this same ideal. Shifters? They let a player play a werewolf. Deva? Half-angel. Wilden? Half-plant, baby.
By putting races like this in the PHB, I felt like WotC was saying, "People want to play to this, so you better figure out a way to deal with it, DMs." I'm of the always-say-yes school of DMing, so if you get a party consisting of one half tieflings and one half dragonborn, so be it. It's up to you as the DM to remind players that just because they picked a core race from the PHB, that doesn't mean they're common or accepted. Feel free to have primitive lizardmen cower before them as gods, or for well-meaning elves to attack the 'monsters'. Have the powers-at-be act as general, racist dinks, and have small villages to shutter up their windows when the conquering heroes breeze into town.
Just because you have a dragonborn or tiefling in your party, that doesn't mean the whole world has to like them. Heck, it doesn't even mean that you as a DM have to like them. But you do have to be able to deal with them. If the dragonbon were errata'd away into oblivion tomorrow, I think you'd still have players trying to roll up humans with scaly wings and ophidian eyes and, yes, even dragonbewbs. By having them be a standard race, the players can play their favorite 'cool race' without having it be terribly overpowered or underpowered or complicated.