i don't think that would work well in SS, for several reasons:
1) weapon mounts have very differing firing angles, and the weapons themselves have wildly varying range and accuracy. so for a ship like the Aurora, for example, the dps at the front left could be quite different from the one at the front right. similarly, a ship might have high HE dps at range 450 (Assault Chaingun) but no HE dps at all beyond that range, even if it has other weapons that do fire at range 600-1000.
2) adding all the dps of PD weapons to the overall number would be useless for most loadouts, but some aggressive ones do use weapons like Light Machine Guns or even Vulcan Cannons for assault roles.
3) some missiles (like Harpoons) have very high dps but very low ammo, meaning they probably shouldn't be part of the overal dps number, whereas other missiles (like Pilums) can fire continously for a long time, and probably should be part of that number.
4) against armor, the per-shot-damage stat is just as important as dps, due to the way armor damage reduction is calculated. so a Heavy Needler might add more dps against shields and hull, but a Hypervelocity Driver might do more dps against armor, despite both doing kinetic damage.
5) an important part of how good a ship is at dealing damage are its flux capacity and dissipation. crazy high dps with a loadout that can only fire for a few seconds can be much worse than average dps with one that can fire continously.
all in all, Starsector ships and combat mechanics just have too many variables to make simple numbers like "this ship can do this much dps" useful. if anything, such numbers could give a new player a wrong impression of what makes a good loadout.