It's the opportunity cost. At low and moderate speeds (we're talking delta-Vs of 10 km/s and less), the same tankage simply gives you higher performance with chemical propulsion, so for no size of tankage may it actually be advantageous to use an NTR instead of a chemical engine. Only at extreme delta V levels do NTRs actually get better performance, but that's not a mission-to-Mars territory. LANTRs could possibly lower the crossover point, especially with variable Isp, but properly estimating how much requires calculus of variations, as I already said elsewhere.
> As to fuel - don’t get it from heavy bodies. Mine asteroids, minor moons, whatever.
Same issue. Your supply may be limited and/or require effort to extract. NTRs throw oxygen away; hydrolox and methalox engines use it for propulsion. For every tonne of water extracted, you'll go MUCH further if you go chemical, or at least with LANTR instead of NTR.
Why is that not mission-to-Mars territory? You can shave months off the transit time with >15km/s delta-v.
2) Intercept velocities, on the other hand, are progressive -- pretty much for the same reason, combined with Pythagoras' theorem. At one point you stop being able to aerocapture, even with exerting downward lift in Martian atmosphere to prolong the braking phase.
Owing to these two things, I'm not quite sure that propelling yourself from LEO to Mars at 15 km/s would be a good idea, unless you intend to crash into the planet.
Using a Hohmann transfer orbit [1], you get from Earth to Mars in about 9 months.
Using an Aldrin Mars cycler [2], you can get in as little as 75 days. Of course, the Aldrin Mars cycler requires more delta-v, but that's the point, if you have more delta-v you get there sooner.