In your opinion, does a breeder need to prove their dogs can perform their breeds' intended purpose? Should a dog that can't do their intended job be excluded from being bred? Would you purchase a puppy whose parents were strictly pet or show dogs?
I think for this it depends on the reasons you are wanting a dog and the lifestyle you are planning on having with said dog. For me, I want to do performance type sports such as agility, disc, etc. so I want a dog that will be structurally sound, good health in the lines, sound temperament, etc. so titles and other ways of "proving" a dog is important to me. I don't care if the dog does the job they were originally bred to do, but rather have the drives and structure and agility to do things that should make it a successful sport dog.
I personally would not buy a puppy anymore that is strictly pet/show dogs... Unless those people were very out of the norm for what I normally see, and more along the lines of my viewpoints.
For companion dogs/dogs without purpose, do they need to be shown or titled in obedience, CGC, agility etc?
I think having titles in stuff is one way to show the ability/soundness in a dog. That hopefully it shows the temperament is sound, or structure, etc. however, I also know dogs that skimmed by. So it's not a guarantee by any means. And there are so many factors that contribute to what a puppy is going to turn out to be like..
Do you consider obedience, agility etc "real work" that should be bred for?
I think it is real work, it makes the dog think, they need drive just like any "real" job.
Does a breeder need to compete with and title their dogs in these sports/jobs (sheepdog trials, hunt tests, etc), or is it okay as long as the dog does it at home? Do they need to be exceptional at their job to bred, or is an average working dog okay?
I think it depends on the titles vs at home thing. It's always a plus to have the titles, but titles can be different than really going out and hunting for example. So it depends, but as long as you trust the dog was worked enough at home or there is some proof, I think things like hunt tests aren't necessary. I would still prefer to find a breeder with them though. But again there are so many things, I would be willing to budge on some things if I found a breeder that did most of the things I find ideal (health testing, 2+ year guaranteed health contract and if something was seriously wrong a replacement pup-without having to return existing pup, titles, I really get into people who do a ton with the puppies as they are growing up (new places, surfaces, water, toys, interactive things, starting training, people, kids, dogs, other animals, etc etc.) to get the puppy started on the right track). There are so many things and odds of finding a breeder that is going to be 100% perfect in every way is unlikely.
So I think you have to be realistic about why and what you want to do with a puppy and research to try and find a breeder that will probably create a puppy that will be closest to what you are looking for. And everyone is going to have different priorities of what is most important that the breeder does. So it all depends.