I think there are a few dangers here.
First, the thing that pops into my head is that this would have to be all or nothing. You wouldn't want one PC to have a trait unless all the PCs had a trait, and those traits would have to be at least roughly balanced with each other. So, if one character had a Gladiator, another had a Multiclass-Wizard, and another had a Half-elf trait, all of them would have to be roughly equivalent. This is a tall order for such disparate ideals, each of which has a different goal behind it. The gladiator trait was designed as a character background, the multiclass for character breadth, and the race for character definition.
Of course, Prestige Classes started with much the same noble goals. We saw what can happen, though, where things can get way out of hand. I'm not saying that makes it a bad thing. It's just something to watch out for. Power creep as well as bloat are things that can tank good ideas.
I'd drop half-races from this. It doesn't seem worth it, and with the options afforded a trait over 30 levels, your half dwarf might end up more dwarf than a dwarf! Not to mention that does that mean half-elves can't be multiclass? That's crazy talk for anyone coming from ye olde editions. Lastly, traits are more like subclasses anyway, and races are not thought of in that context currently in the game. I could see them being implemented like that in the future or in an alternate system, but it doesn't seem to fit right now.
Traits would absolutely make a better multiclassing system, though. When I think multiclassing in 4e, I don't even think feats, I think hybrid. I haven't seen anybody multiclass using feats since hybridizing came out. I think this would be a much more elegant solution. Each class, upon release, would have a short multiclass writeup as well, or maybe it would be imbedded in the class writeup somehow. Then if you wanted to multi- into another class, it would all be right there for you.
I also think I'm going to now use Traits for my 4e Planescape games when I start one up again for Factions. They fit in perfectly with that idea, and I could see them being a great tool. They fit so much better than Paragon Paths or feat trees, or Backgrounds, or anything else I have ever thought about trying. Traits are... clean... that way.