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.