There is so much that is going on between the mother, siblings and the puppy. For one thing the mom is teaching them to play correctly. Also how to be patient and respectful. I watch mine closely and it is amazing. She also teaches them to love and be close. After they have played they have quite moments where they will get close and touch one another - they also use their paw and mouth to touch one another is a very sweet way. Humans cannot not do this in just the same way - it is different. Yorkies are terriers! I have seen some pups of others and it just seems like something is missing with them. It is hard to put it into words.
But besides the training they get from their mom staying longer - the pups get an extra booster. I know that would be more money the breeder would have to pay out on a litter, but I think it is better. Also while they go through that they are still home and would not have to go through more stress thus reducing a chance of getting hypoglcemia. Think about it this way - the pup leaves younger, stressed out due to new environment, then they go to the vets with new owner - more stress, then they get a shot - added stress to what they already have - and some do not eat when they go to their new home - more stress. No wonder all these young pups get stressed out and get sick. As a breeder to my pups - I do not want them to ever get sick or stressed out - Reason I keep my longer added with them being terriers and best to have that longer relationship with their mom - you want them to be very well adjusted pups. So I hold on to my till at least 12 weeks. And yes - the YTCA does say to keep pups till they are a min. of 12 weeks because they feel it is best.
Yes, keeping pups longer would mean more work cleaning up after them and more money with an extra vet bill for the extra booster - but it is doing what is best for the pups, in my opinion.