Well, there are a couple of problems with this conclusion. One is that it assumes that those 10^22 opportunities are evenly distributed in time and space. Another is that we might not be alone, but we might also never meet our neighbors.
The universe hasn't always been a habitable place. It's been hotter and more chaotic; life may have arisen and become extinct due to radiation or cosmic-scale collisions a billion times on a million worlds over the universe's early history. We don't know exactly where the lines are, but we're fairly certain at this point that the universe is not static in time and it has had a less habitable period and will probably have a less habitable period again.
We also don't know what the prospects are for long-term life in environments like galactic cores. Of the hundred billion galaxies we've observed so far, maybe only the tiniest fraction of them are capable of supporting life in the long term -- recall, it has taken Earth 4.5 billion years to produce us! -- and of those that are capable of supporting life, perhaps they can only support life out on their edges.
These amount to some pretty significant polynomials added to the Drake Equation, and they can attenuate the result a lot.
But let's imagine the AI swarm, the most popular rebuttal to the unforgiving conditions of time and space. Let's imagine that one arose a billion years ago, and it happened right next door in cosmological terms -- 1000 light years away. Let's forgive that we are now 71 light years farther away from it than we were when it arose [1], it's fun to mention but a rounding error in this imaginary scenario. You still have the incredible problem of maintaining a homogeneous density of AIs over a rapidly increasing volume! Let's figure one lonely AI to a solar system's worth of space in 1000 light years in every direction -- that works out to 2.6 trillion little self-sustaining devices! [2] With "only" a billion years available to cover that volume, 2,600 new AIs have had to come online every single year (on average) and somehow teleport to their proper location. On Earth, it's easy for us to manufacture 2,600 pieces of complicated electronics in a year -- all it takes is the collective efforts of millions of people to mine the raw materials, refine them, design components, manufacture them, and ship all those molecules back and forth across the globe some absurd number of times. In space, this is much harder.
And this is, I think, a very generous treatment of the AI swarm thought experiment. It assumes that each node has an indefinite lifespan, and both communication and travel are somehow instantaneous over great distances, and that all of the necessary raw materials are always nearby, and that the entire thing never goes to war against itself, and that there are no cosmological disasters (like a GRB) over that billion year span, and that it all happened right next door to us in our very own galaxy. This is the best case scenario for an extraterrestrial presence in our solar system!
[1]: Approximation of the universe's rate of expansion * 1 billion years * 1000 light years of distance, https://www.wolframalpha.com/input?i=70+km%2Fs%2FMpc+*+1000l...
[2]: Volume of a sphere 1000 ly in radius * astronomical units per light year / 100 AU, https://www.wolframalpha.com/input?i=%284*pi*1000%5E3%29%2F3...