is there a specific purpose PSK has that I'm not thinking about?
This allows a Client and Server to re-use Session Keys from a previous session in a new session. This spares the Client / Server from re-doing Asymmetric math and re-sending Certificates (although, see below regarding Asymmetric math).
In this use-case, the PSK is a session key derived from the older, previous session. This replaces the Session ID / Session Tickets based Session resumption that existed in TLS 1.2 and prior.
They called it PSK so as to also innately supports deriving keys from other mechanisms. This will be rare, but it would allow something like IKEv1 derived key and TLS protected data. Or something.
I'm not as familiar with PSK configuration but wouldn't that mean TLS 1.3 still is allowing the use of some form of non-ephemeral?
But, TLS 1.3 also allows the use of resuming an old key and still performing an additional Diffie-Hellman key exchange to "mix in" with the old key. This maintains forward secrecy such that a compromise of the old session keys does not compromise the new (resumed) session.
This does involve using Asymmetric math in the new Session. But maintains forward secrecy between the two sessions.