Logline
Captain Burnham and Book journey into extradimensional space in search of the next clue to the location of the Progenitors’ power. Meanwhile, Rayner navigates his first mission in command of the U.S.S. Discovery, and Culber opens up to Tilly.
Written by: Johanna Lee & Carlos Cisco
Directed by: Jen McGowan
I don't think that's far-fetched - I probably wouldn't be Space Googling the alternate versions of my loved ones.
As for it being the Enterprise...I guess it's to give us a bit of closure regarding Spock's rebellion. Personally, I think it would've been fun to have seen the modified version of the Defiant that was teased in season one.