It's easy to feel, if you own a purpose-bred pedigree, that pedigrees are superior in every way. They are reasonably (if not entirely) predictable in terms of overall look, size, coat, colour, overall appearance, drives and temperament. They are more likely to have been health tested than crosses or random mongrels. It's usually very much easier to track their ancestry and find out about their forebears. If you are carefully selecting a dog that will fit the life you can provide for it, and will be free of certain health conditions, a pedigree is a slam-dunk.
But....
(and there is always a but....)
Problems come with pedigrees too. Because of the focus of some breeders on winning prizes in the show ring, the dogs can be bred to extremes of appearance which damage their health and comfort. The desire for consistency of type or trait leads to inbreeding. Closed gene pools lead to inbreeding.
The problems that result from this are not immediately obvious. A few generations of breeding for a flashy stride that judges of that breed consider gives the dog 'spark' and 'presence' (or whatever, I don't show, I just watch Crufts sometimes) probably won't do a lot of damage over 2 or 3 generations, but keep at it and the breed will have a ridiculous stride, shoulder arthritis by age 6 or some nasty recessive disease will have popped up due to lots of keen breeders going for sires from the same bloodline who provide the deeply-desired 'proud strut so typical of this wonderful breed'. This is an invented example, but you get the point.
And inbreeding and closed gene pools... a bit of inbreeding here and there, an outcross, a bit more line breeding to fix type, probably nothing major going obviously wrong for 20 or 30 years. Likewise a closed gene pool, all looks okay for a century or more.
But eventually, issues will crop up. Every mammal on earth carries random genetic cock-ups. Restrict genetic variety, and some of the recessive genetic cock-ups will collide with identical genetic cock-ups, so you end up with diseases named for breed or types (off the top of my head, wolfhound rhinitis, collie eye anomaly, shar pei fever) or breeds in which certain dodgy genes are prevalent (those causing mitral valve disease in Cavs, for example).
Every mammal on earth needs a diverse immune system. Breed within a closed pool and immune systems will become less diverse. This is probably what underlines the high rates of cancer in some breeds (though genetics also plays a part). Pet insurance companies have no skin the game as regards pedigree vs. cross vs. mongrel, so they crunch the numbers. Work in the US found that labradoodles had much lower rates of cancer than labs and poodles, and golden doodles had much lower rates than golden retrievers and poodles.
So in that sense, pedigrees are a gamble. I love my pedigree dogs. I love their traits, how they look, how they behave. But I am very aware that keeping the gene pool closed isn't good for them in the long run, which is why I'm alert to COI when I get a puppy, and would be in favour of other genetics being brought into the breed.