to answer the actual question though:

I'm not sure if ECDSA can be used to encrypt, I thought it was only possible to use it to sign with? (the DSA part breaks out as Digital Signature Algorithm)

ECDSA can't encrypt messages, only sign signatures.

It would be unwise to have permanently recorded plaintext messages for everyone to see.  It would be an accident waiting to happen.

If there's going to be a message system, it should be a separate system parallel to the bitcoin network.  Messages should not be recorded in the block chain.  The messages could be signed with the bitcoin address keypairs to prove who they're from.

Yes, it's a technical limitation.  Sending by bitcoin address enters the transaction into the network and the recipient discovers it from the network.  You don't connect directly with them and they don't have to be online at the time.

I very much wanted to find some way to include a short message, but the problem is, the whole world would be able to see the message.  As much as you may keep reminding people that the message is completely non-private, it would be an accident waiting to happen.

Unfortunately, ECDSA can only sign signatures, it can't encrypt messages, and we need the small size of ECDSA.  RSA can encrypt messages, but it's many times bigger than ECDSA.