Breeds are templates of certain characteristics. The breed standard sets out the things that should be there (or not be there). The registry then issues papers that certify that an individual horse meets the standard of the breed.
Sadly, I don't know of a North American gaited breed that has a tight breed standard that is routinely enforced. Most are pedigree registries that only track parentage. They say nothing about what the individual horse is. This means that "breed shopping" in the U.S. Can be a very frustrating affair.
Still, even when the breed registry lacks any sort of breed standard (as is the case, for example, with the TWH) papers might be an indicator of performance. They may not be a very strong indicator, but then they also might be. It depends on the quality of the breeding in the line. At the end of the day it's certainly better than nothing even if it's not any sort of "guarantee."
Horses are individuals. Horses are also very able to inherit and pass certain specific traits. The smart buyer educates themself on which traits they want to have in a horse and then does research to find out which breeds tend to have those traits. Then the shop for the individual.