I'm playing this right now and I love the wren, and I can't help but think that if the Wren's built-in tac laser was a quietly custom, 0-flux generating tac laser it would make it a beautifully synergistic ship. It would give you reason not to load the wren out with 5 tacs, since you'd lose the benefit of the built-in 1,000 range laser maintaining the speed boost, thus giving you reason not to exclusively get the Wren when you want 5 tac lasers and also gives you something to really build around because no other weapon other than the tacs (which as I've mentioned equipping loses the benefit of the custom tac) can reach its built-in's range
edit: oh and you could reduce the ship's base dissipation rate accordingly to make it a 0-sum change
Hmm, perhaps, but I try to avoid edge-cases as much as I can. The point of the built-in Tac Laser is to compensate for the fact that the Wren doesn't actually have a lot of weapon potential, even with the customization options offered by a pair of universal hardpoints.
Compared to a lot of other frigates, the Wren doesn't really have a good place for a "main weapon". The Tac Laser provides some semblance of
firepower focus as it were. I'd considered removing it and swapping it for a (possibly hidden) small missile hardpoint and making the front hardpoints from universals into ballistics, but then I've made an Alastor with one less turret.

So for now it's just a main weapon that you can't change. Making it generate no flux seems strange and, if I'm honest, more inconsistent that I'm willing to allow.
Btw, on a similar note I'm thinking about changing the front mounts from universal to composite, because I'm worried about people cheesing the Wren (and also naughty over-use of universal mounts on my part). Thoughts? Would that ruin the Wren for people, or would it be an easily-accepted nerf?