It's only when you realise that getting off Mars is far more like getting off Earth than getting off the Moon, that the full rationale behind SpaceX's obsession with a re-usable launch vehicle rocket that can land itself, becomes apparent.
So much Earth infrastructure we depend on for this stuff.
Why would you need to do that? Why not land the Falcon (Edit: Actually, it might be a Raptor) with the Dragon already on top of it?
It's not even designed to stay in LEO, they go out of the way to make sure it falls back into earth's atmosphere within a orbit or two (often less than a single orbit).
You want to design a new craft from the ground up with the job ascending from mars. Ideally to save weight you want the stage's rockets to be used as many times as possible: Mars ascent, Mars Landing, Potentially orbital manoeuvres to get from LEO to mars and maybe the final part of earth ascent.
But making a rocket fire that many times requires the ability to refuel, perhaps even twice (both LEO and on mars). You also have to be confidant about re-igniting the engine that many times over 5+ years.