Beyond that it can be incredibly useful, when not taken in the direction of raising them as a pet, to preventing certain diseases or parasites from proliferating. Diseases like rabies, when untreated, have a near 100% mortality rate just as an example and many of the parasites out there that affect wildlife can also infect us and are especially dangerous to our kids. So even in just the scenario of helping to take care of wildlife it's beneficial to us as most wildlife rescues will treat what animals they get for parasites and will deal with them if they're rabid.
Arguably taking an injured animal out of the wild to keep as a pet is harmful for its ecosystem. Predators have a major portion of their prey being made up of injured or sickly animals. By saving said animals you're taking resources that they'd otherwise have. However if the animal is sickly because of something like mosquito poison, like what was mentioned before, then taking them out of the wild is beneficial in that case. Many of the kinds of poisons that we use will accumulate in predators and cause them major issues and it'd be cruel to cure them and then set them back out there as a disabled, fucked up critter to just go and get eaten.
In the event that it's an animal from a species that is otherwise struggling then it can be very useful in terms of conservation as they can be set up in captive breeding programs. The parent may be fucked up but their children may not be and could be released to help the struggling, wild population. It's important that such measures are done for those cases as genetic bottlenecking can lead to major health concerns or even communicable cancers like
CTVT(the link has a dog penis in it, you have been warned) in dogs or
facial tumor disease(very graphic, you have been warned again) in Tasmanian devils.
Even if you disregard both cases and it's an animal that is not poisoned, not from a struggling population and you're keeping it after rescuing it(or it otherwise can't be rehabilitated) there is a case that can be made about furthering our knowledge of their species by keeping and taking care of them. Additionally so for raising awareness for them, as even telling your friends about them spreads awareness for what they're like. Who knows, you posting about a quirk of your exotic pet that people don't otherwise talk about may catch the eye of a researcher and lead to some nice discoveries.
In the case of
Chinese hamsters they were of great use in disease research because of their ability to catch many of the diseases that we could. Their cells are still very often found in molecular bio labs in the form of
CHO cells, which play a crucial role in medical R&D amongst other things. With Chinese hamsters though, a major problem when they were still new to the field, was that they were hard to get to breed. In this case, an exotic pet owner who keeps them would be very useful in speeding up the process of utilizing them. Asianometry actually has a great documentary talking about them on Youtube, here's the video:
In general I think wildlife rescue is a good thing, but that most of it should be done with release in mind. I wouldn't stop people from owning wild animals though, I like the system as is with permits being required as it raises the barrier of entry and in general makes it so that people who genuinely care and are knowledgeable about said animal are taking care of it.