Animals fast on purpose to facilitate healing? Do you have a source for this? I suspect some are forced to fast because they are too injured/ill to obtain food.
A positive impact from entering a massive caloric deficit when the body is actively burning calories is counter-intuitive.
Not GP. I don't remember where I read it about wild animals, but my dog would have the occasional "low energy, don't want to play" day, followed by a couple of days of not eating, and then being super-energetic when he went back to eating.
On one of these occasions, I took him to the vet, who said he had a fever, likely of viral cause, and that him losing appetite was perfectly natural and likely helping him heal.
When I'm sick I lose my appetite (and don't eat, sometimes for a few days).
The positive impacts of fasting are supposedly due to increased efforts by the body to scrounge and scrape for calories, which up-regulates processes that have the effect of clearing undesirable built-up matter/cells/etc.