I own, show (conformation and have shown obedience), judge, and very occasionally breed. I have co-owned all the puppies I have sold. I ask only to be consulted if they are bred, and of course my signature would be required if they were bred. One reason I have required this (in addition to maintaining some control over breeding) is that, in the event of the death of the owner, it would apparently easier for me to get the dog back, although of course that is also in the contract.
I have also purchased a number of dogs on a co-ownership basis, and have taken some and given some as stud puppies (ie when other breeders have used my stud dogs or I have used theirs) and have always co-owned those puppies with the breeders.
Another reason we co-own is so that if that puppy were bred, if she is a bitch, and I got a puppy, I could then show that puppy in the Bred By Exhibitor Class at dog shows.
I’ve been doing this for forty years, and so far, it has worked out very well. I am fortunate in having dealt with great people, we all have the dogs’ best interests at heart, and everyone seems to feel the co ownership arrangement can benefit everyone.
In some breeds, it is very much what responsible breeders do. I can’t see how it is disadvantageous to the new owner, if it is done right. The new owners become part of “The Family”!