I used to take care of what some would term “wild” animals and others “exotics.” I spent a lot of time and energy keeping them healthy and sane and did a pretty good job in that our animals all stayed healthy and attractive, and some even adjusted to being around humans.
However, it was a huge amount of work. Now that I am retired I stick with the standard dogs and cats. It is so much easier to care for them properly, and it is much, much easier to find a vet that actually knows how to treat them. We do have one vet in town that used to work with small exotic animals in a zoo (mostly lemurs) and another that used to take care of crocodilians in a zoo, but most local vets stick to cats, dogs, cows and horses.
BTW, I would never walk a crocodile or even an alligator on a leash. They never seem to develop any bond with people and would bite you just because they could.