Would also provide radiation shielding.
The way I usually picture Mars settlements being made is either finding an existing lava tube and creating an airtight seal on the interior, or digging a hole in the ground, erecting a dome (possibly out of blocks made on-site from local materials), and then burying it in dirt. The dome acts as a compressive structure, and you can inflate a habitat on the inside like blowing up a balloon. Either way, people live underground for the benefit of radiation shielding. And either way, the airtight seal of the habitat has something solid for all that air pressure to press against.
Realistically, though, I wouldn't expect pressure to vary that much with elevation. Mars' weaker gravity implies that it would vary less than on Earth. However, according to this [1], the pressure does vary a lot by season. That's interesting.
> Surface pressure: 6.36 mb at mean radius (variable from 4.0 to 8.7 mb depending on season)
Surface water might not be readily available on Mars, but ice is present on the surface at the poles, and probably elsewhere in shadowy craters or underground. (Unfortunately, the places with the best access to ice are not great for solar power.)
[1] https://nssdc.gsfc.nasa.gov/planetary/factsheet/marsfact.htm...