To answer the astronomy things brought up early on:

Hellas basin is not in an ice cap

Phobos is not actually in a polar orbit.

The ice caps are primarily CO2, not water. The ice caps by and large sublimate in reality, not melt.

I remember when part of the reason that I thought Destiny's focus on our own solar system would be cool was the possibility of imparting real knowledge on the side.

I mean, OK, by all means, compromise on scientific accuracy for gameplay reasons, like the amount of gravity on the Moon, and have the Traveler do terraforming for story reasons, but what's the reason for the above?

Unsure.

Turns out I was wrong, BTW. The ice caps are actually mostly water ice. I was remembering some outdated knowledge.

Fairly recently we assumed there was some water ice on the caps but they were primarily CO2, because as they sublimate, we see huge CO2 geysers, and a good portion of the atmosphere drops into the ice caps. In the summer, it goes back to the atmosphere. Now, they think there is a lot of water ice in the caps and a thick layer of carbon dioxide over it.

This change in the atmosphere used to be considered a primary cause of the planet wide dust storms. I'm not sure if that is the case any longer, since most dust storms come from the Hellas Planitia, as we have found out recently through probes.

The impact crater is huge, deep, and covered in a thick layer of dust. It's so big and deep that the temperature at the bottom is regularly 10k warmer than elsewhere. Hence, this difference in temperature and atmosphere can turn into a local dust storm, which goes planet wide.

We can explain away Phobos: Psion Flayers are keeping it where it is, and presumably they just moved it. It's actually in an equatiorial orbit in the real world and if orbiting anywhere near as close as it is in the game, tidal forces would have smashed it up. It's considered to be a loose pile of gravel covered with dust giving it an appearance of a whole rock from a distance.

Using apologetics, we also can explain away the ice caps. If Mars was terraformed, a lot of water may have been in the atmosphere. As the terraforming failed, we may still have a lot of water remaining on the surface, but Mars itself has reverted to being cold as butts. This means that there may be a lot of water ice in places we don't find much of it in the real world.

As I alluded to in reply to Morpheus, there are some unique features in the crater, which I didn't expect to come into play, but now I think may do so.

The bottom of the crater is so low, and it's location temperate enough, that it's plausible that briny water may exist in liquid form during the day in summer.

If we assume that the Hellas basin has retained a much thicker atmosphere, it's possible that it would have a lot of ice there in the Martian winter, as a remnant of the terraforming, and it would not sublimate, but simply melt and refreeze. Currently, the Hellas basin does have a lot of ice in it.

The ice cap comment may just be deeJ seeing ice and thinking it's in the ice cap.

Or, if we really are apologetic, if Mars retains a lot of water, but inexplicably little temperature, the southern ice cap, which is highly variable, may extend even as far north as Hellas Planitia in extreme circumstances (it's as far away from the equator as we are in Detroit and Boston).

Or, going beyond reason, if the orbital tilt of Mars increased significantly from its current 24 or so degrees to around 45 degrees, as has happened in the past, ice would not accumulate near the poles, but in these temperate areas, like Hellas Planitia. Indeed, it's one of the reasons it's considered to be ice rich now.

So, why Hellas Planitia? Well practically, it's the only famous place left on Mars. The moon has tons of famous places: Bay of Rainbows, Oceanus Procellarum, Mare Frigoris, Mare Crisium, they can use those and two dozen others. Mars has 3. The Tharsis region, Valles Marinaris, and Hellas Planitia.

But also, like I said, it has some interesting features. Dust storms originate from there fairly often, so they may want that to be a mechanic. They wouldn't occur with water around, so we'll need advanced apologetics to explain that shit away, which I'm too tired to think about. There's evidence of flowing water in that area. There's weird terrain indicative of large amounts of subsurface ice, but I must stress, this is SUB SURFACE.

The subsurface ice may be interesting to them because of the tunnelling hive, but I'm not sure.

Frankly, I would bet on none of these things: they threw a dart on a map and picked that spot, then made up features of that spot.