That hasn't been demonstrated. Project Orion was canceled before critical parts of technology were actually tested, and the mechanical viability of a pusher plate that has to absorb the impact of several nearby nuclear explosions in rapid succession is somewhat doubtful.
They did do some survivability experiments at ground zero at atomic tests and found that some materials could stay intact. I recall reading that the biggest problem on paper for Orion was cooling the plate in space so it wouldn’t melt after a few pulses. I think they posited various ablative shielding materials plus some kind of active cooling. Of course also remember that once you are in space you don’t need to fire rapidly. One boom every hour or two or even longer would be fine. It could take quite a while to build up to cruising speed, and to decelerate.
Acceleration would require several times more charges since you have to accelerate all the deceleration fuel. With interstellar flight you have two massive problems: going fast enough, and then slowing down at the other end.
100 more years of R&D is not very long on geological or cosmic time scales. My point is that the math working for something as brute force as Orion makes the difficulty of interstellar flight a problematic answer to the Fermi paradox.
I wonder how much such a mission would cost in terms of total Earth resources. I've read Dyson's book on the project some years back and I don't remember that being mentioned.
Wikipedia states the cost in percentage of U.S. GDP (0.1 - 1% of yearly GDP), but I feel like the millions of tons of copper and fissile material required would be significant hit on remaining mineral reserves. It's kind of hard to justify sending out a few missions if it means that the planet left behind is out of easily mined copper and uranium deposits.
We could probably send a probe to Centauri for the price of one Iraq war.
Of course launching “the devil’s pogo stick” from within our biosphere would be rather horrible for the environment. It would be a lot better to build a base on the Moon and launch it from there. You wouldn’t need to burn as much power getting out of a big gravity well. The Moon, being formed from the same stuff as Earth, certainly has fissile material, and it may be closer to the surface and easier to get there.
I really think the most likely answer to the Fermi paradox is that extreme intelligence is rare. There probably isn’t a single great filter per se. It’s probably just unlikely for an environment to be simultaneously stable enough over billions of years to produce high intelligence and interesting enough to stimulate its evolution. Most interesting environments will be unstable, and most stable environments uninteresting (a.k.a. having low Shannon information content).
The universe is probably full of microbes, simple microbial colonies, and maybe a few worms and bugs, but there are probably not very many minds around capable of harnessing the atom and plotting orbital trajectories. Fewer still may have the motivation to invest in such an epic and likely one way journey.
For the latter point keep in mind that solar systems are huge. There are enough bodies and resources in our solar system to keep even a spacefaring humanity busy for millions of years. No necessity to travel to the stars for quite a long time. Space is called space for a reason.
Pricing planet-sized stuff like this in monetary value is problematic.
Taking figures from a quick Wikipedia search, "one Iraq war" buys you 10 years of world copper production at current rates. That is a non-trivial portion of planetary minable reserves, estimated at "from 25 to 60 years"
Then there is the potential of things like hibernation, or AI that can just turn itself off. The latter would be able to use a less costly but slower propulsion system.
I really don’t think travel implausibility works as a Fermi paradox answer. It’s hard but not hard enough to explain the absence of visitors in a galaxy full of planets in habitable zones.