There may be good reasons to do that, but this isn't one. Any project using CocoaPods will still remain working for the foreseeable future - you'll just not get new updates to dependencies at some point. And at that point you can migrate to SwiftPM or vendored dependencies, without losing anything.
Good idea let's punt it to 20 years from now when the CocoaPods server goes down. By then the startup will have been acquired and we will be long gone, so it's the parent company's problem not ours.