Use bitcoin blockchain as a way to send messages to another address purposely setting a 0 fee or a very low fee?
This is possible, but there is always a chance your tx will confirm.

As a drawback, the blockchain is public, so the entire world will be able to view your message, assuming they know what to look for. You can encrypt and fragment your message, but using the blockchain to transmit it seems inefficient compared to other available options.

What is the advantage to using the blockchain, as opposed to another channel of communication?