Of course they do, the latter especially.
And my original post was a rebuke against the notion that big stakes, heroic adventure is a new fad. And my point is that it's been a part of the franchise DNA all along. So 'broad strokes' absolutely matter because they encompass all the stories into a single defining trait. As I alluded to in my last post, the hero's journey is written write into the franchise chorus. Its core conceit is a metaphoric hero's journey for all humankind.
And as I saw where the discussion was headed, I wanted to nip it in the bud before any "Discovery is not Gene's vision" bullshit crept in. Let's look at Gene's vision for a minute and the three stories that serve as his blueprint for the franchise: The two pilots and TMP. Heck, let's go crazy and throw Man Trap in there as well. All of them fit very neatly into the Campbellian framework and all have a clearly-defined antagonist. TMP has world-ending stakes. And one could easily argue that WNMHGB does too (in a theoretical/philosophical/metaphysical sense).