Mongrel dogs have the best of their progenitors

Mongrel.
What’s an awful name for a dog. A dog not belonging to any recognizable tribe of dogs. A product of an accident. Incidental dog. Oops-dog. Dog-pariah. My dog-loving nature shakes with horror.
I go to a local bakery often and frequently ask for a bagel. The one I like the most is “everything bagel.”
I think the name “everything dog” would be much better for the dogs with the less-than-documented ancestry. You can claim he has the best of all predecessors.