"If this stuff happens only once every 1,000,000 years, as we are are repeatedly told..."
On average... over eons. Extinction events aren't like John Kerry or Slow-Joe Biden saying something stupid, occurring on a predictable schedule. A comet hits sometimes every 12,000 years, sometimes every 3.86521478 million years.
To get a sense of time... Stretch your arms out. This is represents the timeline of earth's ~4.5 billion-year history. The distance from your left fingertips to the wrist of your right hand represents the pre-Cambrian (pre-complex-life) period. All complex life on earth exists in the time represented by your right hand. And "in a single stroke with a medium-grained nail file you could eradicate human history."*
* John McPhee "Basin and Range" as contained in...
And, yes, I believe in God... and comets, and asteroids, and meteors.
No kidding. I understand the concept of averages. What you seem to miss is that it is highly unlikely that something that happens every “on average” once in a million years would have happened only 1-100 of that time in our past, immediately after which civilization began. Either it happens more frequently, or we are a result of the event itself, or a combination. Put another way, what is the likely-hood that our civilization followed immediately after the last extinction? We are a result of the event itself.
Or, if you like time lines. Envisage a time line reaching from the dinosaurs, in LA, to the present day, at Ground Zero in New York, this happened 6 block away or half a mile, not even across the Hudson river....
Consider that carefully.