Dogs are usually bigger boned and slower than Fox, except maybe for the pure speed dogs. My guess is Coy Dogs have a hard time catching Fox. A skinned Fox, without all the fur, looks a lot like a Whippet or a small Greyhound.

Pure Coyotes are fast and I have rarely seen many Foxes in Coyote country. Coyotes are also diggers and likely dig the Fox kits out of their dens. The same in Europe, where you see Jackals you see few Fox. Off topic but around here we have Fox overload, 400 miles to the south east and you see more Jackals and Lynx than Fox. Sure there is some overlap, but the tendency seems to be to kill off predatory rivals. The European Yote is about the same size as a large Red Fox, but the Yotes have stronger jaws.

Studies say the Southern Red Wolf is 80% Coyote now, they also say it is 50% dog, which leads me to believe they really don't know what the heck it is. Evolution in progress.

They say since the reintroduction of Grey Wolves in various places, the Coyote population is down around 30%. My guess is the Coyote numbers would be even lower if the Wolves were a little faster or there were more Wolves. If they did much interbreeding, one or the other would eventually disappear or morph into a new sub species.

A side note, Coyotes and Fox are both heavy disease carriers. Some studies say 60-80% of them have Tapeworms. Many have Hookworms. Not the type of animal you want hanging around in the same territory as house Cats or Dogs who might bring a surprise home to your family. Self preservation says you want to encourage them to avoid Humans and human habitation.