Tully was co-owned, and Pirate is co-owned, so clearly, I would.
I think it depends on why, and who you're co-owning with. I've heard of situations in which it's gone really badly, and obviously, in my case it's been great.
I'm wary of contractual obligations towards breeding, whether it be a co-ownership or not, and many co-ownerships are about breeding. Breeding is a
huge undertaking, it can be really tough on the breeder, and I don't like to see people pressured into it. Plus, there's considerations about how it's decided if the dog is even worth breeding. I know someone who got a bitch from one of the "puppy back" pyramid scheme people (sell bitches, require the bitch be bred and that a certain amount of puppies come back, take bitch puppies, sell those under the same agreement....) When my friend decided the bitch didn't really have anything to offer the breed, she had to pay for her again to allow her to not breed the bitch.
In my case, Tully was co-owned because her breeder sells all her pups on a co-ownership, until they are altered, to avoid indiscriminate breeding. I wouldn't have had a problem with that, though in fact, I also didn't pay for Tully, her breeder gave her to me. There were no other real stipulations. She asked me to put a title on her, but that was kind of a joke, because she knew I would anyway. I thought she might not want me to breed Tully, but when I started considering it, I discussed it with the breeder, and she was fine with it. Provided mentorship.
So, obviously an ideal co-ownership from my standpoint, all the benefits were really to me.
I put Tess into a lease in both our names when she was bred, because the original idea was that we'd each get a pup from the breeding, and she wanted to be able to show in bred by. As it happened, there were only the 2 pups, and my co-breeder decided Eva wouldn't suit her purposes (I had tried to get her to take first choice, but she insisted that 1st choice should be mine). I felt bad that she didn't get her pup, and I hadn't even paid a stud fee, so I offered to co-own Pirate with her. That's why he is co-owned. As with his grandma Tully, he's basically my dog, but he has someone else's name on him as well.
It all works, because we're friends, and we have similar goals and beliefs about the breed. We don't agree on everything, but our points of disagreement are relatively minor. We don't have a contract, which is generally not advised, but I'm not expecting any issue from it, and since I have physical possession of the dog, the power is all mine. (though it's not impossible I'd send him to her to be shown. I trust her, though.)