Such a mechanism would make complex life even more rare in the universe. Better this solution to the Fermi paradox than that sentient species tend to destroy themselves with technology.
If the GF is in front of us, in a universe with lots of ETI, our chances of evading it are extremely small. After all, no one else has; why would we be so special?
Nick Bostrum has called detection of ETI, or even complex ET life, the worst news mankind would ever receive. It would be a death sentence for our future.
Great distances and inherent speed limits seem like a decent way to accomplish that.
Now, perhaps it's universally true that civilizations don't advance much beyond where we currently are, or don't persist for sufficiently long for interstellar colonization to be successful. These would also be very depressing outcomes if they are imposed on us by the GF.
When a colony ship arrives to a new planet, it'll need to bootstrap a full industrial chain before it can build its own colony ships to expand to other systems. It's reasonable to assume there would be little incentive for that before the colony starts to require off-planet resources on their own system, and, therefore, has a compelling reason to build a space economy. For us, this would easily be in the thousands of years even if no terraforming is needed, and let's not even consider we'd need a consistent multi-century planning to get there. Precursor missions with automated in-situ resource collection and storage would allow colonists to arrive to a fully built and stocked colony, which would save some time. Existing biospheres might present issues of toxicity and biological risks: you really don't want to grow up on a (Dune's) Rossak (even if it grants you superpowers).
So, let's say Earth manages to establish 10 successful extra-solar colonies over 5 thousand years. It'll be at least a good couple thousand years until those successful colonies can each establish 10 others and raise the number to 100 worlds. If we manage to diligently expand at that exponential ration, we'll soon bump into other intelligent space-faring species that also share this commitment to reproduce.
Here's a good place to start:
https://joshworth.com/dev/pixelspace/pixelspace_solarsystem....
Signals diminish with the square of distance. SETI would never hear anything from other stars unless it was broadcast with insanely high transmit power or was directed right at us (and still very powerful). Nobody would do that unless they knew someone was here actively listening.
https://briankoberlein.com/blog/et-phone-home/
So for example, to reach the Centauri system (the nearest star) with a signal as powerful as the signal Voyager sends to Earth would require a transmit power of over 100 megawatts at a minimum. That's just the nearest star. It gets exponentially harder as you go further out. For more distant stars you're talking gigawatts or terawatts or beyond.
Even barring concerns about attracting attention, why dedicate that kind of resources to operate an interstellar border blaster if you don't even have a reason to think anyone's listening, and if you won't get a reply for hundreds or thousands of years?
If you are going to sterilize Earth you might as well just terraform something dead. This isn’t even getting into the ethical questions, just looking at practicality.
If you’ve got the technology to come here, well, you might as well terraform something dead. We almost have the technology to terraform Mars (albeit over thousands of years) and it seems easier to do and possibly faster than interstellar flight.
Building giant space station habitats is also easier than interstellar flight. Uploading brains to machines, which would allow settlement of almost anywhere, is probably easier than interstellar flight. AGI is probably easier than interstellar flight.
In fact interstellar flight is so hard it might rarely be attempted anywhere by anyone unless there’s a forcing function like one’s star becoming unstable or some other cosmic scale calamity. Solar systems are huge and contain vast amounts of resources.
That could mean a lot of things including just chance. There could be galaxies out there that have in fact been fully colonized.
Imperialism usually burns out after a while as the cost begins to exceed the benefit.
I could see a universe of mostly steady state civilizations that experience occasional bouts of expansionism or the sending of things like the Nauvoo from The Expanse. But those are transient events. This would greatly increase the time required for the galaxy to become saturated with life as per Fermi paradox models. It might happen eventually, meaning if we wait long enough some alien Mormons might show up. (The Expanse reference.)
Then consider that intelligence is probably a recent (on cosmic time scales) phenomenon due to metallicity. Previous generations of stars and planets probably lack the mineral diversity to support complex intelligent life.
There will be strong selection for expansionist cultures and species. As long as the universe is mostly unoccupied, expansion means increasing your share of the total population. Relatively static cultures will simply become irrelevant compared to their expansionist competitors. The experience on Earth recently is in the context of a world where all places that can be occupied (at the current tech level) have been.
The selection effect will operate at the biological level as well. Currently on Earth birth rates are declining. Modern civilization is acting like a kind of pesticide. But like any pesticide, it's going to select for resistance. This will likely mean more people will have an increased desire to have children. Selecting for this may take a while, but on the time scales involved in this thread it would happen very quickly.
In the long term, all societies in which selection is allowed to operate will push up against limits and be in states of Malthusian equilibrium. To counter this would require an unreasonable uniformity of control across time and space. All ET species, at all points in their history once they can undertake colonization, will have to exert rigid control on their societies and biology. Any defections from this uniformity will explode exponentially and overwhelm those who are not controlled.
Metallicity is not a good argument, since there are zones, even in our own galaxy, with higher metallicity. Closer in to the center, for example. https://www.nature.com/articles/s41550-023-01977-z
Why couldn't there be a very large number of low-probability filters and/or a continuous probability of failure spread across billions of years? Add them all up and the cumulative effect would be the same as a single great filter, but there would not be one single primary hurdle that needs to be cleared.
This and the Fermi paradox itself are really just speculations. We have only one data point, which makes it impossible to say anything definitive.