Well, its the gate to the Asteroid belt & even has two asteroids full of resources in low orbit! Not to mention having and a (thin) atmosphere and usable gravity, that also opens a lot of opportunities (aerocapture, no micrometeoroids, easier thermal control, etc.).
Why do you need to be on Mars to do that? It's simpler to do everything in orbit, which is the real gate to the asteroid belt. Or directly establish bases in the belt, if we knew how.
Yes, that's also certainly an option. Still, it seems to me that a lot of people still can't really think in terms of space only infra and "a hight tech city, but on Mars/Moon" gets them to a more familiar context.
So I think it makes sense to talk also about surface bases, to get more people on board, even if those are potentially quite inefficient.
Yes. This.
I hope that we piggyback on Mars exploration for building infrastructure on the Moon.
The Moon is a much better target for a first self sustainable colony and also could become economically interesting.
There is nothing on Mars that is economical interesting AFAIK.