Assuming you would never want double fire tool, the current system allows for 5 different engineering sets. If you include the Pipe/Mallet loadouts, the proposed system would allow for 6 unique loadouts. if you don't, you've cut it down to only four useful loadouts. Not a significant difference in loadout choices for engineer.
I think that the most important thing for crew is prioritisation. Engineers must juggle repairs, rebuilds, fire suppression / prevention, spotting, shooting, and buffing, all with tight, efficient movement while making use of cooldowns and anticipating damage.
Gunners have to shoot, spot, and still repair things, depending on ship and situation.
While engineers may seem overworked, I think it's more simply a difference in priorities among the classes (and more accurately, roles on the ship).