Once that inert liquid is into every single component on the engine how do you safely and cost efficiently remove it?

What inert liquid wouldn't vapourise at least partially under the force of a rocket engine?

Mostly though you can't find a nice friendly pool of inert liquid on Mars or anywhere else but the Earth in our solar system ;).

Probably because a rocket engine is pretty hot on landing, so the thermal shock upon contact with the liquid would deform it or cause cracks.

There's no pool of inert liquid on Mars.

When you look at any design out of SpaceX, you need to keep in mind the fact that Elon himself drives the requirement of 'this has to help humans get to Mars'. It extends through the Falcon, the Dragon and a whole heap of other aspects of what they do.