As mentioned in other comments, you have to trust Apple to hand you the correct public keys. They could easily MITM you and decrypt the messages on the server if they misrepresent the other party's public key. Additionally, the iMessages you send are signed by your private key, which is probably not something you want.
Because they can be used against you and you won't be able to deny the message has originated from you, which is a desirable security/privacy property in a messaging app setting. OTR, and mpOTR[1] in particular, try hard to remove non-repudiability from messages.
To be clear, it's a desirable property that parties engaging in a conversation are able to verify authenticity of messages and that they indeed originated from their authors. It is undesirable that the parties of the conversation are able to definitively prove to a third party, not involved in the conversation, that a message was indeed originated from a specific person.
