Redundancy is incredibly helpful with fixity for a couple of reasons.
One piece of fixity information isn't infallible. Even checksums can be defeated through collision attacks. For that reason, it can be helpful to store more than one type of checksum such as both md5 and sha-256 and/or other fixity values like an oxsum, file names, and file system metadata.
Different types of fixity information require different computing resources. Running and comparing checksums on a million files will take a significant amount of time. It's much cheaper to generate an oxsum, compare file names, and check file modification metadata, than computing checksums. It might be advantageous for your workflow to check those cheaper values frequently and use them as an indicator whether to run a full checksum routine, in addition to less frequent but regular full checksum routines.