It's not that you can't blast at one another in the Space Assault map, it is that people are too lazy to read what the mission objectives at the start of the round.
I never played Space Assault while it was available - didn't even know it existed - but Shantytown can be really disorienting your first couple of times through. Sure there's that pop-up telling you what to do, but if you're used to Arenas and you see the rest of your team are already running off ahead of you, the instinct is to just close it out. I admit I had no idea how it worked until I goggle'd it, after my team and I got our aft-ends handed to us.
IMHO, it'd be helpful for newbs to have a sort of mini-tutorial on the different kinds of PvP maps.
As for why nobody played space assault, I'll go with the theory that it was way down at the bottom of the queue list - back when said list was 2-3 times longer and more complicated than it is now.