Can I just butt in with a question on why that is? To me it seems that if Bitcoin uses public-key cryptography to transfer ownership of the coins, it should be a trivial matter to include a short message that is only readable by the recipient.
Almost but not quite. Bitcoin uses EC-DSA, which can only do digital signing, not encryption. RSA can do both, but I didn't use it because it's an order of magnitude bigger and would have been impractical.