When you don't have a need for a cryptographic digest, it's important to think of the channel's bit error distribution in selecting a checksum algorithm.

Different checksum algorithms can provide better error detection for specific channel error models (potentially even with fewer bits). Non-cryptographic checksums are typically designed for various failure models like a burst of corrupt bits, trading off what they do/don't detect to better match detection of corruption in the data they will protect.

For example, if you know that there will be at most one bit flip in your message, a single bit checksum (parity check) is sufficient to identify that an error occurred, regardless of your message size. (Note that this is an illustrative example only, since, typically, messages have a certain number of errors for a certain number of message bits -- the expected number of errors depends on the size of the message.)