Symmetric-key ciphers aren't used because they "save a round trip". They're used because they're much faster. One could use a public key encryption system to encrypt the entire session between two parties (e.g. RSA) but AES is much faster than RSA.
Speed is one concern but far from the main reason. You couldn't use a typical-length RSA key to encrypt a large chunk of data because there's a max input size for any given RSA key size. Standard block/stream cipher modes of operation are defined only for symmetric key ciphers.
The max input size is for one message. It's effectively the "block size" for RSA. You can send multiple messages using a single RSA key (and in fact pretty much everyone does that, otherwise you'd need a new public key for every message). RSA is a complete crypto system, you don't need any additional ciphers. You do need randomiziation (e.g. random padding).