wild animals have evolved to live with parasites - they use mud, the services of birds plus rubbingon trees, anthills and boulders to rid themselves of the pests.
Also, domestic pets live in close contact with humans and we don't like to be infested with ticks, worms and fleas.
In certain game parks they put feeding stations that have a rubbing pole tht has a tick muti on it and when feedi g the animals rub and scratch themselves against the pole and ge the anti tick muti on themselves
simple answer is that they don't live cheek by jowl with humans. Its the humans who don't want to pick up worms fleas and ticks and the ensuing parasite born diseases. In the wild if the parasite burden gets too much then the animal dies tout court.
They get all of those parasites. Worms are the biggest problem as fleas and ticks drop off eventually. Most wild animals can get by with a small worm infestation, but when the burden gets too high they die at periods of stress, such as winter or during droughts or get caught and eaten by predators who are probably a part of the parasites life cycle.
Generally, animals can tolerate a certain amount of parasites without any problems. It is not in the parasite's interest to weaken or kill the host. Parasitic worms and tics/fleas need to leave the animal at some stage - either as eggs or larva - to complete their life cycle. Wild animals have a huge habitat compared with domestic ones, so the likelihood of multiple re-infestation is smaller.