That may be how the creators of the show came about their reasoning 'after-the-fact' for including Pike, but that's not how it is played out in the episode.
They didn't write that reasoning into the show.
They wrote it as Pike commandeering the Discovery ONLY AFTER the Enterprise was incapacitated.
Which clearly happened after the Discovery was already on its way to Vulcan.
Which can only mean he wasn't the Captain that was supposed to be at Vulcan.
Pike took command of the Discovery in the manner he did only because the original circumstances under which he was to have done so changed.
This is made pretty clear by what he says, and, as I noted, by what the producers and writers said on After Trek last year about their decision to have the Discovery and Enterprise meet.
So you're denying that the writers knew that Pike was going to take command of the Discovery when they sent the ship to Vulcan at the end of WYTMH? even though they explicitly stated on After Trek that they crafted that episode and the rest of Season 1 specifically around the moment of the two ships meeting?