"It's heavy, and any accident would render a chunk of Mars radioactive for quite some time."
If you model the rest of the universe out of Earth's highly protective environment as "already being the result of a major nuclear accident", you're not actually that far off. The people evacuated from Chernobyl received about 33 milli-Sieverts of radiation [1]. The surface of the moon gets about 60 micro-Sieverts of radiation per hour[2]... or, in other words, being on the surface of the moon for 20 days is the rough equivalent of experiencing one Chernobyl disaster. This is just a rough estimate for intuition purposes, it's not exactly the same radiation in both cases, but it's close enough to make the point. This page [3] says the surface of Mars is about .7 milli-Sieverts of radiation per day, for about 30 micro-Sieverts per hour (to use the same units as the moon above), which is about right for the inverse-square and slows the exposure to one Chernobyl per 40 days.
And by universal standards, that's still rather low radiation. There's entire galactic clusters with the central blackholes blasting sterilizing amounts of radiation out into their entire cluster. Earth is fairly special; a good reason not to mess it up. The "jump to Mars plan" is perhaps not impossible but it's really, really, really hard.
[1]: https://nuclear-energy.net/nuclear-accidents/chernobyl/chern...
[2]: https://www.space.com/moon-radiation-dose-for-astronauts-mea...