Most if not all exotics/zoo/wildlife residencies require at minimum a 1 year internship or equivalent practice (what exactly that means depends on the program). That is a minimum requirement though, many people do multiple internships. Basically agree with what jayna said about training, networking, research, etc. It is very competitive because there are very few programs and a decent number of people interested in them. Somewhere around 15 total zoo residency programs in the US and Canada, and only about half of those take a resident every year, the others only take one every 3 years.
Internships are slightly less competitive. A lot of people will do a small animal rotating or large animal rotating, and then an exotics or zoo-specific internship. Some end up doing multiple. I know someone who has done 3 different zoo internships while trying to get a residency (a lot of people will apply for specialty internships and residencies at the same time). There are a couple of programs now that combine small animal ER/rotating and zoo internship. Again those are very competitive because they are attractive to students who want to start getting the specialty exotics training without having to do a whole year of 90% small animal. I don't know of anyone who has gotten one of those positions without significant research experience, publication(s), and excellent grades.
Match rate for the last few years (aka matched applicants/total number applicants):
2020 - Exotics/Wildlife/Zoo internship: 17% Residencies (zoo specific and exotics/zoo/wildlife combined): 7%
2019 - Internship: 13% Residency: 7%
2018 - Internship: 13% Residency (there were only 7 total programs in these categories that year): 5%
There are some zoos now that do their own 1-2 year internships separate from any academic institution, those are outside of the match so not sure on stats.