I think for a piddle pad trained dog, discrimination is the problem. We have hardwood floors and don't have a problem with Sadie. We had a lot more problems when we had carpet. Bathroom rugs are a disaster and thank goodness they are washable. When we travel, the first thing we do is pull up the bathmat. Otherwise, we end up washing it. Sadie does like her privacy to poop. I keep a piddle pad in our guest room and our dining room for that purpose. She will go into another room to poop. The other thing I've noticed is that although she squats to poop while on the piddle pad, more often than not, there is a little trail of nuggets that fall as she trots away from it.
Beemer - oh Beemer. The downside of a non-neutered male! I kept him intact because he was a show potential puppy and I agreed that if he turned out, I would try to take him in the ring. Last spring I finally declared (with the help of my breeder) that he is not going to be a show dog (he's small and his hair isn't good silk, and his color isn't clearing). He was 18 months old by then and pretty set in his marking ways. He does pee on the piddle pads - I can tell because he squats to do that. It's the marking that makes me crazy. Luckily he has a couple of favorite spots and I keep a piddle pad kind of wrapped around that particular furniture. To his credit though - he is really good about pooping on the pads. I'm getting ready to schedule his neuter and maybe I'll get lucky and the marking will get a little better.
Both of mine stay in playpens (with piddle pads) when we aren't home so that's not an issue. When we travel or he goes to someone's house, he wears a belly band. It seems to work pretty well.
I've had a lot of dogs over the years but no Yorkies. These are my first piddle pad trained dogs. I agree with Nancy that it's harder for a dog to learn that it's ok to go to the bathroom in the house - but only on a piddle pad than it is to learn that you never go in the house. Except for Beemer's marking, my dogs are pretty well trained and it's good enough for me - I don't need rugs.