I like certain purebreds because of the way they look, same as I pick a mutt pup because of the way it looks. Temperament comes into it after that for me. Though as a general rule, I am a lifer so regardless of temperament my pups have a lifetime home with me. My current dogs have vastly different temperaments in some ways and then in other ways they are similar (probably a by product of the way they are raised). At the end of the day, if I dont like the way a dog looks then I am not going to buy one. I am not a fan of poodles (great dogs, just dont like the look) so I personally, would never own a poodle, or a poodle x because of this.
I dont disagree about the health issues, and that is something I have focussed on in talking my friend out of buying a cavoodle from a breeder who has performed no health testing. I think you will find most people would be in agreeance in regards to health testing.
Sure, soe people might rehome because the coat didnt tuen out how they wanted, but that is not the majority of owners. I would say the majority of "designers" end up in a life time home where they are loved deeply regardless of how they turned out. What we see in shelters is a small percentage of what is actually bred.