That's just it - there is no privacy. You've got a client which stores plaintext messages server side, just waiting to be broken into by (hackers/government agents/kiddies). The messages are being sent unencrypted unless you enable the "secure" (it really isn't) mode anyways, so we can also add "people who can sniff your traffic" to the list of adversaries.

That's pretty much the polar opposite of "private".