Chapel having to explain her feelings for Spock to the alien was kind of a teenage show thing. BUT the more I think about it the more I realize that TOS had aliens with simple, sometimes pure, goals. So I think these aliens fit right in with ST.
The “ancient alien” line may not age well. They are usually very careful not to put references to our time due to it not dating well (Musk, Stacey Abrams). I’ve heard it mentioned on Shuttle Pod show that the actors could not change a word of dialoge to protect the show from sounding of our time. Of course the joke of using that phrase will fade so maybe it’s OK.
What was that bit about Pike’s girlfriend looking for Dilithium? Was it a joke that went over my head? Could someone explain?
I agree about reference to our time, but the Lorca’s Musk line works because he’s from the mirror universe. I’m not sure that’s what the writers intended, but I’ll take it.