I admit, a lot of them are stinking gorgeousbut there is always the whole moral implications of what you are really doing for the species, considering most hybrids result in a lot of deaths and bad eggs! So it can be frustrating as well as heart breaking.
The dog thing is a little off(although some recent studies suggest a few jackals and coyotes contributed to the blood lines slightly depending on the area of the world--sort of accidental breeding and mixing as other wild dogs/wolves were also 'domesticated' at the time), but actually Betta fish come from hybridizations of separate speciesBetta Splendens never existed in the wild, they were created by man mixing several wild species of betta. Many color morphs are actually created mixing splendens to other wild type species! The difference is many of them seem closer related, and though they are different species, they tend to all breed pretty easily, other than two things-- the fact that they are different sizes and often have trouble 'wrapping' the female(though eggs almost always are just fine), and the fact that some breeders try too hard to keep a strong line and overbreed things like thick scales into an animal that isn't meant for such thick scales, causing scales to form over the eye, blinding the animal. But that is more about bad breeders than the hybrids.
But it's a very touchy subject. I know I myself would not go into breeding them! I know a lot of people worry about the blood line of snakes being muddied, but people sell hybrids for so dang much, I really doubt many people could get a hold of one without knowing it was a hybrid! If they got popular and less expensive I can see that being a problem, though.