Do we have any concrete figures on an entire rocket designed to use this engine? Like, mass fraction, etc.? Because if you look at the engine in isolation it seems good, but that's ignoring all the shielding you'll need and the huge fuel tanks because your propellant density is so low.
I'm just an armchair space enthusiast, but both of those problems seem like they have possible workarounds or solutions. Using methane instead of hydrogen could significantly reduce the required tank volume since CH4 is denser, and you don't lose that much performance with it (based on Project Rho's table linked above). For shielding, if you put the fuel mass between the engine and the humans aboard, you should be able to get a decent amount for "free".
It's not clear that methane would be as workable; that's a large change from hydrogen to that. We at least know that hydrogen is workable, because an engine was built and tested.
As for the shielding, you can't use solely propellant as shielding because you still need shielding once the propellant is exhausted (the engine remains highly radioactive after having been used). And it's not clear that hydrogen provides suitable shielding for all the kinds of radioactivity generated here anyway; you might actually just need lead. Plus you still need substantial shielding in the event of break-up/crash on launch.
At what distance is radioactivity no longer an issue? The engine could be attached to payload at a longer distance with relatively lightweight structures. It doesn't have to be designed to stand up to the stress of launch/land with a payload. Just to ferry between points in space.
It's definitely worse than H2's ISP in an NTR, but ~600s is still a solid boost over the ~450s that's about the best a practical LOX/LH2 chemical engine can do.
My curiosity is essentially just whether the performance lost between an H2 and CH4 NTR would be gained back through reduced tank mass and boil-off. Shielding/engine mass will certainly be a big mass penalty versus chemical rockets.
Hydrogen being less dense causes a problem (not solves one) because the fuel tanks need to be much larger for the same propellant mass, and thus you're adding a lot of structural mass.
Well, there was the Saturn C-5N [0] - basically a Saturn V with a nuclear upper stage instead of another J-2. That increased the payload to LEO from 118,000kg to 155,000kg. (and an even larger increase in mass to TLI/TMI/etc)
It may not be something we know yet -- based on reading the available materials it doesn't seem like we got past the stage of designing the engine on its own.