Plenty of Star Trek stories have involve existential crises.
Absolutely, but it's not frequent in TV Trek. TOS directly threatened Earth less than five times (The Alternative Factor and The City on the Edge of Forever are the only ones I can think of offhand). TNG waited until Best of Both Worlds. DS9 and ENT had existential threats to Earth, but only one per series. VOY dabbled in them with the Borg and Species 8472, but week-to-week, crises were appropriately scaled as involving the ship and crew.
And what do you mean 'quick succession? We have to wait at least 12 months between seasons.
Imagine if the DS9 writers decided to solve the Dominion War in the third season, then introduced some new antagonist (Pah Wraiths, Breen, etc) every season thereafter. Do you think that would have been better than what we got? Don't you think people would be bored with the "boy who cried wolf" aspect - and the artificiality of the single-season conflicts - by the end of the series?
I mean, I know the idea that each season arc is separate and involves its own "bad guy" goes back to Buffy (though I've personally never seen the show). But speaking personally, it just seems way too formulaic to me to get invested.