What are some practical usages of message signing other than proving ownership of a Monero public key?
Proving ownership of a Monero public key is helpful if you solely want to verify ownership but there are other uses. Here are a few possibilities:
"Ownership" and "control" are not always the same thing. A new user may have a Poloniex Monero address which they "own" but a potential donor trying to encourage new users to set up full nodes may require a signed message to verify control of an address before a donation is sent.
Communicating details relating to a business transaction is another use case. Merchant can use the message signing feature to confirm a package was sent, including a tracking #.
Suppose a buyer regularly sends monthly payments to a wine buyers club. One month the merchant suddenly changes its Monero address without warning. The buyer concerned about a possible MITM attack, could ask the merchant to sign a message confirming control over both their old public key and the new address.