I suppose it does help the vet put the children through college, but it is a combination of the fact that the animals are at more risk of lethal diseases (it is harder to tell whether an animal is sick, and what the problem is, than with humans, harder to control the opportunities for infection, and we are less likely to put them into intensive care if thiings go bad. )  There also are more diseases that need repeat shots and more animals in circulation that are not protected, thus increasing the risks attendant on low herd immunity, than is the case with humans in first world countries. (Though there are certain criminally irresponsible people who are trying to sabotage human herd immunity!)  We cannot put our cat into his favourite cat hotel without up-to-date shots, and we like it that way; it means that he is unlikely to pick up infections from fellow-guests if they cannot pick things up from him.

There is no special tendency for pet microbes to mutate especially rapidly, and if they did, that would not require more frequent shots. It would simply make most kinds of shots fairly useless fairly soon.

You don’t need now, but you did when you were a child. Even now, as an adult you are in a risk of getting lets say tetanus and as a child you received several doses of the same vaccine, it is not that today it is a different, mutated sort of tetanus with a different toxin, it is just that your immune system forgets stuff and needs reminders from time to time.

Like mmmm says, your immune system needs to be "reminded" (boosted) about some diseases like tetanus at regular intervals. Same for pets. Some diseases also do mutate frequently ... the best known is flu ... many people have an annual flu vaccination (actually a re-vaccination not a booster) to cope with changes to the virus. It's a war out there ... the viruses and bacteria have many possible strategies for getting in, and we (and all living things) have many possible strategies for keeping them out.