If we started pursuing nuclear pulse propulsion we could have our first probe arrive in the next star system in a hundred years or so, and eventually get the travel time closer to 40 years.

If?

Theoretical is still theoretical. We have no functioning propulsion that can exceed what the probes are currently travelling at.

At least for something like Project Orion, all the individual components are either verified in prototypes or proven technology. We have existing stockpiles of nuclear bombs. Propelling a craft by exploding something behind it is demonstrated in smaller prototypes with TNT. We know how to do radiation shielding, we know how to do shock absorbers.

Or course combining technologies in a new way comes with lots of engineering challenges, but it's a smaller leap in technology than e.g. the first moon landing.