Oh, nothing. You simply can't show them in a lot of venues.
I mean, you can get an ILP number on them and do Obedience/Rally/Agility and so on, so it's really not a huge deal.
Just the competition homes that I know have a preference so that they can go on to register them w/ other kennel clubs and compete in their venues too.
It doesn't make them any lesser of a Yorkie to own! You should get one!