Both breeds are very, very rare in adoptable mixed breeds in the U.S. You can read 100 breed profiles in DoggyDNA and never see either.
While certain other breeds are prolific – BC, GP, husky, ACD, the ubiquitous pit, and the popular littles, some GSD, boxer, blue heeler, etc., appear in a significant number of the mixed breed profiles. Working farm breeds tend to crop up regularly.
The reason is dog-owner culture in the U.S.
The most common breeds reported among mixed breeds are those that include owners who allow their dogs to roam unneutered. And regional areas where strays flourish under the radar (there isn’t a big push by the community for animal control to eliminate strays, they are somewhat accepted as a fact of life).
If a breed hits the popular culture radar, it is highly likely that BYBs and puppy mills will push them into the category of owners who will add yet another layer to less controlled breeding.
Whereas the breeds that are rarely if ever seen in mixed-breed profiles are those with protective owner communities who control breeding and almost never outcross. If there is a mixed breeding, they find a responsible home for the neutered/spayed pups.
If a purebred or mixed dog that is visually identifiable as (probably) all or part of one of the highly curated and protected breeds happens to turn up in a shelter, there is a) a unique backstory and b) a good chance that a breed rescue will come get it, if the shelter knows to call them.