Burying a reactor underground is not a cooling solution. Rock is not a great heat conductor. So the reactor will stay cool for a little while, to the heat capacity of the surrounding rock, and then melt because the rock isn't effectively carrying heat away from the reactor.
But not to worry we'll launch them on fantasy rockets! So long as we make the rockets out of Impracticalium rather than Unobtanium we should be fine. We can start tomorrow.
It's entirely possible to conceptualize ways a Mars/Moon/orbital colony could work. The issue isn't coming up with ideas on paper it's the actual implementation of those ideas that is actually difficult. Handwaving implementation details and actual engineering challenges is just writing science fiction. It might be interesting and entertaining but it's not actionable.
[1] https://hn.algolia.com/?dateRange=all&page=0&prefix=false&qu...
As I understand it at least some of them are "walk-away-safe" in case of meltdown, which is conceptually unlikely, and don't need the big cooling towers you speak of.
I know they are not there yet because of materials science, regulation, but they are not science-fiction either.
Anyways, I don't see any reason to not bury them in mars ground, instead of doing so here on earth.
Getting them there would be difficult, but some big effing rockets in their freight configuration should do...
Edit: or some Sea Dragons [2] https://en.wikipedia.org/wiki/Sea_Dragon_(rocket)