Edward knows that TLS sessions start using asymmetric encryption, and then move to use symmetric keys. What limitation of asymmetric cryptography drives this design decision?

Asymmetric cryptography has a relatively high computational overhead, making symmetric key encryption faster. That means that once you can exchange an ephemeral symmetric key, or a series of keys, you can encrypt and send data more quickly and efficiently using symmetric encryption. There is no key length limitation, and reasonable lifespans are met with either technology. Key reuse is not a problem with a public key encryption scheme.