Even if it had no technical value (a fact that I am not quite convinced is true), having a checksum is a very potent bragging claim (even better if bitcoin doesn’t have it).
It allows us to say:
Ethereum has an built in way to validate that addresses are indeed valid addresses, and not just any random string of bits. Before any token transfer, addresses are validated against the embedded checksum and any inconsistency will cause the transaction to be aborted.
Sadly, marketing is important, even for things which make little technical sense.