Starlink would most certainly be of little direct use here.

What I could imagine is having Starlink satellites around Mars that allow to route data from rovers anywhere on the planet to a dedicated high-performance communications platform that handles communication with Earth.

In fact that's exactly what they're doing: the Mars Reconnaissance Orbiter is serving as a communications relay, as it did for previous landers.

It's just that since there have never been more than a handful of spacecraft active on Mars at any given time, there's currently no point in spending huge amounts of money to launch a whole constellation of satellites for continuous coverage.

And a photographer! MRO took what might be my very favorite picture of all time: https://www.space.com/16946-mars-rover-landing-seen-from-spa...

Could be still a nice exercise if someone could compute how many Starlinks could a Falcon Heavy throw to Mars transfer orbit & if they could be able to actually capture into Martian orbit by their default means of propulsion (do they actually have any high thrust engines ?).

Not only the MRO, but other orbiting assets as well, particularly NASA's MAVEN and ESA's TGO. Even the venerable 2001 Mars Odyssey is still used as needed, I think.

Even ESAs Mars Express is still around - since 2003!