>Starship would be better utilized to build a fast human Mars transport vehicle in LEO than being used directly as the crew transport.

I agree, but the way to do that is with NEP, not NTP. Or at least not of the solid core variety anyway; gas core NTRs might do the job, but it doesn't seem likely they'll be a thing anytime soon.

Solid core NTRs don't really get you to Mars any quicker than Starship. With an Isp of 900s and a mass ratio of 5 you're looking at 14.2km/s. Starship with it's 380s Isp and ~12 mass ratio only gets 9.2km/s - 5km/s less.

On the face of it, that seems like a 50% speed increase, which is nothing to scoff at. The problem lies in slowing down at Mars. Starship is able to aerobrake, saving it ~4km/s of delta-v as compared to propulsively braking into orbit.

So there goes most of that 5km/s lead for the NTR stage, and the remaining 1km/s has to be split in two - a 500m/s higher cruise speed also incurs 500m/s more braking requirement - a much more modest 6% speed increase.

You could fit the NTR stage to aerobrake as well, but given the massive size of the tanks and the high dry mass of the NTR, it's likely to suffer a proportionally larger performance hit than Starship paid for the same capability.

 

Now, to an airless body such as Ceres or the Jovian moons it's obviously a different story and the NTR takes a considerable lead over Starship. However, NEP's advantages over NTP grow even more pronounced over larger distances, bringing me back to my original point.

The only real exception is of course Luna, where you can't aerobrake, and it's very close proximity puts NEP at a huge disadvantage.

NTRs perform a bit better if you focus on payload capacity instead of speed, but only in terms of mass fraction. In terms of cost the pure hydrogen and enriched uranium might well cancel out any mass savings if you've got cheap LEO lift. And in terms of ISRU, pure hydrogen is an order of magnitude more energy intensive to produce than hydrolox or methalox.

I'm definitely a Starship enthusiast, but I don't think Starship 'solves all problems'. It solves many problems, and NEP solves most of the other ones, while NTP only solves a few niche ones in between, so I have to wonder if it's really worth the trouble.