Yes - I do think you are right, it is a kind of snobbery and virtue signalling.
So, it's useful to understand how we got the purebred dog system we have now.
Historically, you had certain types of dogs, like sighthounds, or herding dogs, etc. Humans would deliberately select dogs that they wanted to propagate the characteristics of to breed together. You also had geographical constraints. So what you got was a tendency to see certain working types and also geographical types. You might find herd dogs in all kinds of places with herd animals, and they might have some common characteristics, but not be related. But there were no "rules" anyone had to follow, you could choose a very different dog to breed in if you wanted to achieve something (say, a larger dog line.) And lots of dogs just went around and had indiscriminate sex, so people would pick up puppies that had good qualities for their own use, whatever their parentage.
A good example of this is to look at all the small terriers used for the same kinds of tasks in the UK. Their jobs were valuable so people kept them, and you see that slightly different types appear in different areas. But the borders and edges were often porous unless there were strong geographic barriers.
During the Victorian period, some people got the idea that you could create more perfect dogs by defining each of these types according to a standard, which was created by looking at the best example of the dogs (in the opinion of the people who were seen as experts.) They then registered those dogs, and to be given certification you had to show the pedigree of your puppies was entirely from the dogs admitted into the registration. It was no longer possible to cross out, and any accidental crosses weren't admitted either.
Interestingly, some of the working dog breeds were not part of this process, notably border collies. Jack Russel Terriers are another example. For those dogs, as long as they could do the work, they would be admitted to their separate breed societies (or some just didn't even have breed societies.) It was very very controversial when border collies became eligible for KC registration under the KC kinds of rules.
The difficulty with all this is that the scientific theory that limiting to perfect specimens will lead to an improved breed isn't really scientifically valid. At the time the system was created, it was considered to be true. But it's now better understood that genetic variation, including in phenotype, is generally an advantage, that there is no such thing as a "pure" bloodline really, and also that decreased genetic variation can lead to bottlenecks. Eventually this tends to lead to decreased fertility, and also more cancer. (We understand this where humans are concerned so I am not sure why it's controversial when we say it about dogs.)
As for what dogs people breed together in order to achieve some purpose, it can vary but usually they try not to undermine their project. You will see ein some dog-sledding they will use pointers, even though they are not very weather-resistant, but they have some qualities that are desirable. They may cross back several generations beyond that. It can be surprising though - my husband used to have a mixed breed gun dog - and accidental lab-husky mix. She was a fabulous gun dog, though could never have been in trials as she was very unconventional. But for actually hunting she was pretty unmatched.