THere is an easier way to figure this out. It also agrees with what we observe.
If we assume that Earth is not rare or unique and that there are millions of Earthlike planets in the galaxy then if this were true what should we expect? How can we calculate what we would see. Not "guess" but "calculate"
Lets build a simulated galaxy populated with exact copies of Earth but the key is each copy of Earth is made on a different year over the 4 billion years of Earth's existence. So our simulated galaxy has 4 billion earth-like planets and they all have different ages.
What would we see? Out of the 4 billion Earths
1) about 100 of them would be humans who know how to build radios. So radio technology would be very rare. with one
2) most of them would have only microscopic life
3) A fair fraction would have multi-cellular life
4) one in a million planets would have mammals, like mice and monkeys and such
Earth is the only data point we have but Earth has existed for 4 billion years, we can look at Earth one each of those billion years and get 4,000,000,000 data points
This is actually VERY disappointing from a SETI perspective because it means that even of something like 1 in 25 plants has an exact copy of Earth we can expect only 100 planets with radio and perhaps zero that can transmit a radio signal over interstellar distances.
So, bacteria-like life might be common, multi-cellular life would be rare, intelligent life would be a one-in-a-billion level rare and advanced technological life would be exactly zero (as we are not there yet.)
I think this is the ONLY method of prediction that does not use extrapolation or guessing. It makes an impossibly optimistic assumption and then concludes that we should expect to hear and see nothing even in a galaxy teaming with "life". In other words, this theory predicts what to observe.
If you want a theory that predicts that we will find ETs then you have to introduce guess and extrapolations like
1) High-tech societies do not destroy themselves be war or global warming or advanced AI.
2) As societies age they continue to care about the universe around them. We don't know. Perhaps they only play video games and live in simulations.
3) perhaps the biological people are peacefully replaced by some kind of hybrid AI and therefore required very small amount of resource for trillions of them to live and expansion is possible by simply building a one meter cube server room
We have no idea about 1,2 or 3 and any answer is a guess. But if you assume only what we 100% know, we should expect a silent galaxy that is filled with simple life.