The elephant in the room here is that advanced intelligent life as we understand it is some inevitable step in evolution. A random walk of mutations on top of mutations lead us to this and only because the environmental context favored adaptions toward intelligence in the case of our species at the time. This is probably why most sci fi is not written by evolutionary biologists.

Yes, but as time goes to infinity there will eventually be an environment context and mutation path that will result in something that has a similar level of intelligence.

In fact, this makes the preoccupation with humans escaping a Great Filter all the more childish. Even on a single planet the species that will evolve from humans by the time Earth is swallowed by the sun will have less in common with humans than we do now with single cell organisms. Internalize that fact a little bit. Once you realize it is absurd to talk about the human species being preserved as is to the end of time, you will understand the silliness of this obsession. Cause after that point you might as well believe in a deity.

If it makes you feel warm and fuzzy inside, it suffices to hope that only single cell organisms survive the Great Filter, since given enough time it might lead to something that is as intelligent or more intelligent and kind than humans.

Embrace the silliness. The answer to "Why should we humans spread to other planets?" need only be "Why the fuck not?"

That is, unless you want to fund your rocket company. In which case you have to make people believe in a deity.

Er... No that's not a meaningful critique. There's no framework that doesn't assume it's a random process. The point is to find out how likely each step is to occur, randomly.