As I understand it, with what I can remember of my degree-level but a very long time ago genetics, the thinking is that a first cross between two distinct breeds, called F1 in Mendelian genetics, gains 'hybrid vigour' from the mix of the two distinct, unrelated sets of genes.
It's used in agriculture, both in plants and animals.
I think that the North of England Mule is still the most prevalent mother of a fat lamb in England; she's a first cross of a Blue-faced Leicester father on a hill ewe, usually a Swaledale or a Blackface.
The Blue Grey cow is a superb suckler cow for the hill and moor; her father is a Whitebred Shorthorn and her mother a Galloway.
So personally, I have no problem with the trend for crossbred pups in principle. As Labradoodles and Cockapoos become popular, with sensible breeders and good practises, there should be no reason that strains of Poodle good for siring Labradoodles, and for siring Cockapoos, shouldn't become established. But they may well be different strains - a dog that makes a good sire of a labradoodle may have different characteristics to one which makes a good sire of a Cockapoo.
I also have no problem with the naming of crossbreeds, so long as it is applied consistently. In the same way as a sheep advertised as a North of England Mule is certainly 50% BFL on her father's side and out of a blackfaced northern hill ewe, I would want it to be the case that, at the very least, something described as a Cockapoo is a first cross (F1) between a Cocker Spaniel and a Poodle.
With livestock, this consistency, not only of the breeding but of the outcome, is achieved by the establishment of Breeders' Societies for the type of animal. So I would rather see the Kennel Club at the very least encourage the establishment of Breeders' Societies which can be affiliated for these crossbreeds.
