@tabulahrasa
The problem with any of those studies though... is that when people say crosses are healthier than pedigrees they don’t mean pedigrees of any breed, they mean of the two breeds that have been crossed.
Well, yes, sometimes this is what they do mean. But so much depends on the pedigree dogs in question.
Cockerpoos are the crossbred of the moment. Cockers and poodles, apart from PRA, tend to have different health issues. It is either not usual or not possible to test for the likelihood of parent dogs passing these on to their offspring, but since these illnesses are more common in some breeds than others, it's likely that they are due to genetics. For example, there was a poster on this board just recently whose young cocker had a sudden leg fracture to a joint issue that is largely confined to spaniels, so is almost certainly genetic, but which cannot be tested for.
So, yes, a cocker puppy from health-tested parents who are clear of PRA won't develop PRA, whereas a cockerpoo puppy from untested parents might - but the purebred cocker puppy's parents won't have been tested for a suit of diseases to which poodles are not prone. This means that the our notional cocker puppy remains susceptible to all of these illnesses - but it's unlikely that they'll crop up in the cockerpoo. (Obviously if you start back-crossing your cockerpoos things will start to look a bit different.)
As @CovoidOfAllHumanity says, we know the risks of consanguinity, and these risk are the same in dogs. A low COI based on known pedigree is no guarantee that the COI would remain low if the pedigree went back another five or ten generation - and recent DNA research has shown that many breeds are seriously inbred, much more so than current breed COI stats, based on recorded info, would indicate.
Closed studbooks are a blight in the longer term. We'll destroy purebred dogs eventually if we don't allow some outcrossing to bring in new genetics, and that would be a terrible loss.