OTOH, consider the atomic bombs dropped on the cities.
I'm assuming
1. If Cthulhu awakes, we're boned. [1] But he's still sleeping.
2. The Deep Ones are made of meat, as are their monster servants. The bigger they are, the better military targets they make. And their weapons are mostly of the pointy metal thing variety. There are
billions of them, which does give them a bit of an advantage initially in thinly-armed areas.
3. Sure, they have black magic. But Arkham asylum and various third-world witch-doctors are on that. (Remember in the 'Shadow over Innsmouth" the Deep Ones in the Pacific were baffled by a bunch of Polynesians with star-stones).
4. Shoggoths are, admittedly, a problem - which calls for high explosives followed by flamethrower mop-up. The shoggoths that serve the Deep Ones are neither as smart nor as huge as those under Antarctica. (If they were, it would soon be by bye deep ones).
5. The eventual outcome is MAD. We can't find all their cities, and irradiating the oceans would kill us too. Also, they can summon the Outer Gods - which will kill everyone save Cthulhu and any other Great Old Ones lying about. (hey, if a half-non human hillbilly with access to a good library could do it..)
(My assumption is that a modus vivendi will be arrived at before the world is stripped clean and yanked into a violet-lit infinite abyss).
Bruce
[1] My personal no-prize theory? If the Big C just needs somebody to knock on his door for him to wake up, why all the elaborate cultist stuff? No, he slept through the rising and sinking of R'Yleh: he just grew close enough to wakefulness to kill the guys who messed up his ressurrection with a materalized
dream of himself: just good ol' ectoplasm, not cosmic monster-flesh. The
actual Cthulhu sneers at speedboats.