I'm sure I'll be corrected if I'm wrong, but my understanding is that public key cryptography is very processor intensive. Because of this, instead of using you

I'm sure I'll be corrected if I'm wrong, but my understanding is that public key cryptography is very processor intensive. Because of this, instead of using your private key to sign every bit of communication, you use the public/private key crypto to negotiate a shared secret for a different algorithm, such as AES. It's more than just an issue of efficiency. Encrypting/signing nonrandom text with RSA exposes you to all kinds of nasty attacks. For example, if you directly sign a message whose blocks are composed of prime numbers (rather than hashing the message and signing the digest), then an attacker can afterward forge your signature on any message composed of a sequence of blocks which are known powers of those primes or their mod-N inverses.