Then again, the Earth has been home to a variety of active alien horrors for billions of years - how are humanity not dead by the 1920s?
"The Kanakys explained that folks from the other islands might want to wipe the Deep Ones out if they got wind of their being there, but the Kanakys say the Deep Ones don’t care much, because they could wipe out the whole brood of humans if they were willing to bother...."
- "The Shadow Over Innsmouth"
"[The Mi-Go] harmed only those earth-people who got too near them or spied upon them. Animals shunned them through instinctive hatred, not because of being hunted [because the Mi-Go] brought their own food from the stars...."
- "The Whisperer in Darkness"
"The time would be easy to know, for then mankind would have become as the Great Old Ones; free and wild and beyond good and evil, with laws and morals thrown aside and all men shouting and killing and revelling in joy. Then the liberated Old Ones would teach them new ways to shout and kill and revel and enjoy themselves, and all the earth would flame with a holocaust of ecstasy and freedom....."
- "The Call of Cthulhu"
Even when the stars are right - or, especially when the stars are right - human beings simply aren't important enough to bother making dead, or are perhaps too useful or entertaining to make dead (the quote from "The Call of Cthulhu" suggests that, when that time is right and Cthulhu returns, human beings aren't just alive and well - humans apparently become like Cthulhu's kind, apparently sharing all the power and joy and freedom of the freed Old Ones....)
You could just as easily ask why cattle, sheep, dogs, lab rats, and cockroaches are not dead yet in a world where humanity's star has risen; all sorts of animals live not just in spite of humanity, but in many cases because humanity tolerates them or even helps them survive for mysterious human reasons, and that's not necessarily a happy thing for those animals.
Remember that Call of Cthulhu is normally a game full of things worse than being dead happening to a few unfortunate victims in secret, but a post-apocalyptic game of Call of Cthulhu is a place where all those things-worse-than-death are happening at the same time, on a massive scale, in public, forever and ever....
In any case, set your scenarios whenever and wherever it makes you and your group happy. I just wouldn't rush to say "you can't do that" so quickly - some of the best Weird stories are about things that can't be done!