Won't they have the same launch problem on Mars with their engines blasting debris everywhere? I guess a smaller gravity well means less thrust, but it still is a lot of thrust.
However this is a problem that needs more study, the are various projects on how to quickly make a functional launch pad.
[1] To Mars and back diagram: https://www.spacex.com/human-spaceflight/mars/
So far, there has not been public information about what they're going to do about it.
A render of the moon landing Starship showed engines higher up that have been speculated to be used for landing and lunch to reduce the problem.
You need a lot less thrust to get off the Moon’s surface. That probably puts the problem back into a familiar envelope.