Mainly since 3 classes would take quite the effort to implement properly, and on account of balancing.
I agree it would need to be balanced and would need some work to get it right, but that's true for anything new. And since the content is already there, there are only two main parts that need to be balanced.
1. The aspects of each gun need to be buffed or lowered (or stay the same in some cases) depending on their class.
2. The layout of the gun slots for each ship.
And there are already a few light guns that are 'lighter' than the rest. Like the harpoon, flare gun, and banshee carousel.
The heavy ships (galleon, goldfish, and spire) all have light guns to compliment their heavy guns. It would be interesting to give the other ships two gun classes as well without raising them to heavy ship status.
It would also add another choice for captains which in turn makes for more diversified gameplay.