I do think bloodlines are important in a breeding animal. You can have a very nice mare or stallion, "perfect conformation" and lovely movement, but if there is nothing behind that animal then it's a complete crapshoot what that horse will pass on to its foals. Even with a pedigree with one or two good animals, if there's no consistancy to type and conformation, if out of the 4 generation pedigree there are one or two top animals and the rest are mediocre, then there will be no consistancy in the foals. This is a common thing in the Miniatures--lack of consistancy.
In Morgans, line breeding has been very common. In a 4 or 5 generation pedigree you are likely to see the same name several times--or you may see several names which are different but which you know all go back to a common ancestor another 2 or 3 generations further back. Those pedigrees ensure a good amount of consistancy. There are Morgan stallions that time after time sire foals of the same type and quality. Even when bred to mares that are an outcross, the strong genetics of the stallion will show through, and the foal will come out looking very much like all the other foals by that particular stallion. This is considered a good thing, assuming the stallion is a quality animal & sires quality foals. Obviously a stallion that is line bred to a poor quality individual is going to sire consistantly poor foals--if you're going to have a stallion that sires 'rubber stamp' foals obviously you want him to be a good quality animal that sires good quality foals!!
I like to see good breeding in the first 4 generations of the pedigree. One top animal amongst a lot of dogs doesn't do anything for me--I like to know what those 4 generatins of horses looked like, and they need to be animals I like. If it's a non-breeding animal then the horse standing in front of me is what counts, but if I'm selecting the horse for breeding I have to like the immediate ancestors. If the mare is the most lovely creature going, but her sire and dam were two of the ugliest horses I've ever seen then I'm not going to take that mare as a broodmare. It would be just my luck that she would produce foals that were every bit as ugly as her sire & dam combined!! And if her sire & dam are undesirable to me then it doesn't matter to me that there are 3 top names in the 3rd or 4th generation.
In Morgans I have also seen a foal throw back 6 or 7 generations--the colt was nothing like any closer ancestors, he was the spitting image of a stallion back those extra generations. I know others that have said they had the same thing happen--and in view of that it is important to me to have a horse that has as many good horses for as many generations back as possible--difficult with the Minis, because they are a relatively new "breed" with a very hodge podge ancestry.