Remember we're not talking the stone ages here. We're discussing modern day, domesticated horses who are relying on us to care for them in a world making it increasingly difficult to do so. Personally I don't give a hoot about whether or not a horse has papers but if it pertains to breeding, then yes I think being registered greatly improves a foal's chances. Not by much...nice papered horses are going for about 10 cents a pound now at the auction...but at least they still have a better chance.
I think the gist of what a lot of peeps are saying in this thread is not to end breeding entirely, but to just...think a bit harder about it. I know that's not going to change some people's method of doing things (what will? :/). I say if you feel you're responsible enough to consciously choose to bring another life into the world, you should think ahead a little...including all possible "what if" scenarios...as they pertain to the horse that would not have been here had you not decided to breed. It is your duty as a breeder...and what I have been seeing is that lately too many people are breeding without giving thought to the possible consequences of their actions, and they provide the slaughter companies' bread and butter, regardless of their intentions when starting out.