Designer dogs are not hybrids from mixing 2 different species. Most dogs are the same species, just different breeds caused by man inbreeding to develop certain traits.
Chihuahuas, African painted dog, Asiatic dog and Australian dingos are different species of dog and can hybridise with domestic dogs, which are 99% wolf. But dogs like German shepherds, border collies, great danes, papillons, Jack Russel terrier, cocker spaniels, etc, are all the same species so crossing them with each other isn't an issue and can actually help reduce the number of genetic disorders some of those breeds carry.
What needs to happen is governments around the world need to get together and outlaw the breeding, production and supply of deformed animals, birds and fish. If people are going to hybridise a fish, it should be normal shaped and be able to swim, breath and act normally. This would stop the Asian fish farms from pumping out mutated fish like balloon fish that suffer internal problems and can't swim or act normally due to their deformed bodies. It would also stop people breeding cats, dogs and other animals that have short noses and can't breath properly, uneven length legs that increase hip and back problems, etc.
This is slightly off topic but my state government recently asked for ideas about e-waste (unwanted and broken electronic devices) and how to deal with it. I told them to enact laws saying all electronic devices sold in this country should last a minimum of 20 years (like they used to last century). Then the suppliers in Asia would have to make better quality products that wouldn't end up at the tip after a year. I doubt the government will enact those laws but governments need to get off their backsides and start making laws to stop e-waste, polluting vehicles, and deformed animals. If the government doesn't make the laws, nothing will change because some people have no ethics or morals and don't care about anything but money.