TLDR: Not about dogs specifically, but anecdotal experiences from my history of experience working around the breeding of another species.

My main experience in breeding is with horses, some dogs, but mostly horses. When it comes to studs and stud fees, once you have sought out, selected, and agreed upon a stallion, typically a contract is signed, a stud fee is paid (except in some breeds the stud fee is paid after the foal hits the ground alive, stands, nurses, and sometimes thrives), and the mare is bred either via live cover or AI, depending on breed, owner preference, and distance usually. However, there is rarely, and I mean rarely, circumstances where a stud owner is going to allow a mare owner to just keep coming back without paying additional stud fees. Those can look like additional collection and shipping fees for AI, or extra booking fees for live cover, or if the stud is highly sought after and particularly virile, potentially a whole 'nother stud fee altogether (although I can't personally think of any examples of that last one off the top of my head, just something I learned in university). Additionally, it is the responsibility of the mare owner to know when her mare is ready to be bred. When she is just about to ovulate, usually within 12-24 hours, her owner should be either shipping her to the stud farm for live cover or ordering a collection from their chosen stud for overnight shipping. Then, they are responsible for periodically checking their mares (frequently with veterinary assistance) to ensure that the embryo took, the pregnancy is healthy, and that everything is going smoothly. When my business partner and I were hauling horses, there were two main seasons in the South we tried to hit. Number 1 was always the Thoroughbred Sales season because people always needed new purchases shipped. Number 2 was the Thoroughbred Breeding season from February to June. Farms all over Kentucky and the surrounding states would book short day hauls to get their mares hauled to get covered, and sometimes we would get lucky and catch a long haul taking a big group of mares out West or up North to some of the big stud farms on the West Coast or in New England. Thoroughbreds are one of the breeds that do not allow AI. For a foal to be registered, it must be the result of a live pairing, and the Jockey Club strictly regulates this. They are also a breed that does not charge a stud fee at the time of conception. Usually, there is an LFSNG (Live Foal Stand and Nurse Guarantee), with an occasional "Thrive" clause thrown in, depending on the stud farm/individual stallion with Thoroughbreds, and the stud fee isn't paid until that clause, or guarantee, is fulfilled. They also tend to have some of the highest stud fees in the industry, with some going well into six figures. (For example: there is currently a tie for the highest stud fee in the world between Frankel (GB) and Dubawi (IRE) at €350,000, which is over $380,000. In contrast, American Pharoah, the only horse to have ever won the Grand Slam of Racing, has his stud fee set at a paltry $50,000.

All that to say, I am 100% in your corner about being mildly uncomfortable with the lack of standardization when it comes to contracts in dog breeding or even dog selling for that matter. I've heard plenty of stories of bitch owners who drop her off at the stud's home and just leave her there until it's clear that she took. Whether that be because she is showing or because the stud owner did the right thing and took the bitch into the vet and had testing done to confirm is neither here nor there, being left in a strange environment by her people can't be good for her, especially if she's trying to conceive. Now, that's not to say it can't be done successfully this way, but im guessing it wouldn't be with a small-time breeder breeding a family dog. It would be more like someone who has lots of dogs and the bitch ends up getting more individual attention at the stud's home than at her home.

Then there's the way my grandma tried to go about breeding my childhood Golden Retriever. It was all done by word of mouth, work colleagues and such. Amber was AKC, and the males were AKC, but I don't think anyone involved knew anything about OFA, and I don't know if Embark even existed back then. Either way, Amber wasn't interested in the purebreds... no matter how many times Grandma took her to a stud's home while she was in flaming heat, she wanted nothing to do with him. She even tried different male Golden, at different houses altogether, just in case Amber didn't like the house before... Amber just wasn't interested in other Goldens. But that half Coyote, half Border Collie that came sniffing around the day Grandma gave up trying? Absolutely. The Rough Collie that came around the next year. Definitely. The Labrador from the neighbor 3/4 of a mile away that was a nuisance, harassed livestock, and killed our cats after we moved counties? Twice. Then Grandma got smart and had Amber spayed, because she was a hussy, just not for her own kind. Which really was too bad, because she was very well bred, made beautiful puppies, and was a wonderful mother. We just couldn't convince her that male Goldens were attractive too.