As usual with the filters, the problem always is that the filter has to be so significant that it's essentially guaranteed to happen. Else the galaxy should still be full of aliens. We seem to keep scraping by with close calls, so it doesn't seem all that guaranteed that a technological civilization wipes itself out before it can establish itself among the stars.
We've had several close calls in the last ~80 years. I have no idea what the actual probabilities of inciting WWII and causing a nuclear winter were in the Korean war, Cuban Missile Crisis, Able Archer exercise, and various computer errors and false alarms that occurred, but if you're rolling the dice on existing every 10 years, the chances of taking over the galaxy in a million years are remote.
I think you meant WWIII, but it does bring up another interesting possibility—WWII could be seen as the release of pressure which had been building, in some sense inevitable. If we were only slightly less belligerent as a species, we might have been able to put it off until nukes were invented, and what a mess that would have been. If we were only slightly more belligerent, we could have blown ourselves up in the Cold War. Of course, belligerence isn’t a tunable parameter that you can tweak without changing all of history, but it is funny to think that we just happened to land right in the sweet spot.
But none of our technology can really let us spread at this stage. We’re barely detectable from nearby solar systems.
It’s very possible that the technology required to travel between solar systems is where the filter occurs and we’re in a narrow window of having enough technology to look around at nearby planets before we wipe ourselves out.
