So lets start by looking at the assumptions it makes. They are: We've got 13 Billion years of history, and our system is only 4 Billion years old, so everyone else has a head start. There are not only lots of planets, there are lots of habitable planets. We'd see the signs of civilizations that are more advanced than us.
So let's tackle the head start one. At the start of the universe there was just hydrogen. Heavier elements are made in the center of stars, and get included in planets when those stars explode and their remnants eventually make it into new systems. As a result the chemistry of the universe is constantly changing. Solar Systems formed significantly before ours won't have the same proportion of elements. Yes in the planets we can see, we see complicated elements, but a lot of the time we're just seeing things on the lower part of the periodic table. Being sure that there is a head start for planets like ours is a stretch.
What about all the habitable planets? Well as noted above a lot of them may not have our complicated chemistry, and might be ok to colonize if we can bring the trace elements we need, but may not be complicated enough to give rise to life. Beyond that, let's look at our solar system. Mars is in the habitable range, but if it's home to anything now it's only extremophiles. What went wrong for Mars?
It's magnetic field went belly up. That cost it most of it's atmosphere as well as protection from radiation. It's speculated that our magnetic field is the result of the motion of our planets ferrous liquid core. We think that martian vulcanism is dead. So maybe is the mojo in the core that once generated the field. So some would be habitable planets just haver a limited lifetime, after which only extremophiles can hang on. Then there's Venus. Venus has a very slow rotation and no magnetic field. Why is the rotation so slow did it ever have a magnetic field? Venus also has another problem. A runaway greenhouse effect. What did this, the lack of a magnetic field, the long days leading to less localized thermal regulation to begin with. There's so much wrong with Venus, that we don't know where to begin. But of our 3 planet sample, one has life, one could have had life but not anymore, and one had at best a much shorter period of habitability. Again planets like these might be useful to us in the long run but don't serve as sources for the civilizations that we think that we should see. And that's not counting other benefits we have like our moon to give us tides and wind, or the moon and Jupiter to reduce the number of strikes our planet takes. We don't know what portion of planets out there have all these favorable factors but it's far fewer than 100% It would be weird if the majority of potentially habitable planets in our solar system weren't habitable but nearly all others were.
Finally there is the notion that we'd see signs of civilizations more advanced than us. Our use of radio waves has been a blip. Who knows what our future holds, but if we abandon broad spectrum radio waves within a hundred years than that it's just a blip and the notion that we'd be where we are and be at the perfect distance to catch another civilizations radio blip is highly unlikely. And it's really arrogant to project on what we'll be capable of in the future, and thus what another civilization would be capable of. This is the most baseless of the assumptions. We have reason to believe the universe is much older than us, we have reason to believe that there are lots of planets, but until we spot one we have no reason to believe that a remote civilization would be detectable by us for all but a brief window.
So where does this leave the Fermi paradox? Well with a much smaller potential head start for everyone else, and a much smaller percentage of planets that might give rise to civilization, and no reason to think that we'd be able to detect one for all but a brief window, there is no Paradox. The likelihood that we should have ween these civilizations goes from overwhelming with assumptions that are too generous to unlikely with more pragmatic assumptions.
Why does the Fermi paradox matter? And how does changing it's assumptions change that importance? The Fermi paradox matters because of our level of civilization is common/easy but none exist anymore then there is an unknown danger in our future to be afraid of. How does changing the assumptions change this. Well it puts a lot of the ominous great filter before us, behind us. Our system formed when the chemistry was complicated enough, that's 9 billion years of missing civilizations accounted for. Our planet didn't end up with a runaway green house gas before reaching a space littering level, that's all those civilizations from Venus like planets that are accounted for. Our magnetic field lasted long enough. That's all those mars civilizations accounted for. And our moon, and Jupiter and so on and so forth. Much of the filter of the Fermi paradox is behind us. Our civilization has yet to survive a significant asteroid strike or a super volcano, so there's still a chance that it's premature to say that we've made it. When there's a self sustaining population that's not earth dependent that could re-terraform earth in case of a problem, then I would say we're good, until then we haven't escaped all the filters. But after that I don't think there is any reason to worry about any other filters, until we actually have more evidence that we should.