Can I delete message on Mobile Connect?

Once a message is marked inactive after 180 Days it will be deleted by the system. This is covered in this help doc: Inactivate a Message

NOTE After 180 days, MobileConnect archives inactive messages and removes them from view. You can still review information on archived messages in the calendar on the day the message was sent.

Support would not be able to delete any messages within an account

Seems like you can only make the message inactive. If you want to completely delete the message, you may need to raise a support ticket with SFMC, and they will be able to delete it from the backend.

Thanks