The problem with a fingerprint reader is that it’s useless unless you have a way to register, store, and recognize fingerprints, which means having additional chips that do so (not to mention some sort of UI for doing those). That’s why you hear about things like the Secure Enclave in iPhones that handles those sorts of tasks, but those are basically minicomputers running stripped-down OSes, each of which is specifically paired with a matching fingerprint reader.
While it’s theoretically possible, a strictly capacitive button would probably be SIGNIFICANTLY easier.