Ok... this is how I feel on the subject:
First I want to start off by saying... Papers dont make a horse. But:
If I have a registered mare (which I do), and I am goin to breed her... (which i am when she is old enough), I will not breed her to an unregistered stud. I dont know his bloodlines, how he has been shown, how he has placed, how he performs, if he has any babies on the ground... so on and so forth. I can go by what the owner states. But lets face it... not every horse owner is honest.
Now... on the other hand... I have an unregistered mare (which I dont). And if I liked her well enough to get a baby from her I would know where shes been, how she performs, what her flaws are physically and mentally (for exampe if shes a hot head and I want a calm baby, Im not gonna breed her to a hot stud), what problems she needs corrected. And so I can go on and look for a stud that can hopefully "fix" these problems on the foal. I can call up the the registry and track down his current foals and see how they are doing, what they look like, their dispostion.
Thats my opinion on the subject.