This is not actually a solution to the Fermi paradox. The assumption that FTL travel is impossible is built into it. It’s still an unsolved puzzle why we don’t see any evidence. The duration of slower than light travel is not actually a hinderance on galactic timescale. A civilisation that develops successful interstellar travel and starts to spread throughout the milkyway galaxy can colonize it in a paltry couple of million years, and that’s assuming a very leisurely pace of expansion. This assuming that there is no intentional, concentrated effort to actually do it, which would be extremely unlikely to be upheld over such timespan by any civilisation except for relatively dumb self-replicating machines. Those could do it a lot faster. And one of the questions is, in fact, why there isn’t any evidence of those around. They rank among the most probable means such an expansion would employ, and so far we can’t see any evidence that they’re at work anywhere.
Another logical path to take for advanced civilisation is that of dyson swarms, in order to solve the energy problems that will neccessarily arise. The thing with those is that by now we have the capability required to detect them over a range of thousands of lightyears.
In my opinion, there’s three reasonable solutions to the fermi paradox which are slightly less speculative than the others:
One, The future of advanced civilisations looks entirely different than what we can currently imagine. Given our past track record with imagining the future in the light of an unavoidable presentism, I consider this one very likely, but won’t make a fool out of myself by trying to speculate what those civilisations would actually look like.
Two, we simply didn’t have our capabilities for long enough to actually detect anything. Given the amount of exoplanets we’ve discovered at outright incredible distances, this one is becoming more and more unlikely.
Three, we’re among the first. It’s not as preposterous as it sounds. The galaxy needed the first couple billion years just to produce the heavy elements that make our technology possible. While there was ample time for others to arise (and colonise the galaxy) before we ever walked on two legs, the time is not so long that you’d have to consider the possibility inevitable.
All other solutions have more or less big problems, but are in general too depressing for me to really consider while I have more hopeful alternatives, though they do make for great science fiction (for the berserker hypothesis specifically, I can recommend Alastair Reynold’s revelation space series).