I know that hindsight is 50/50, and that what is done is done, but I think these special bridge officers should fill out all three classes.
There's a Reman science officer. Fair enough. The Remans are quite cunning and intelligent in their own right.
There's a Jem'Hadar tactical officer. Makes sense, because the Jem'Hadar were specifically designed for combat. Most of them aren't able to fix or function the finer details of machinery unless they are specifically bred for that function - and they rarely ever are.
And then there's a Breen Tactical officer. That's how it was designed back when the Breen episodes first went live, and that's all well and fine, but they seem like they would make excellent engineers.
Most of the Breen that I fight against usually use engineer abilities such as spawning medical generators. The Breen are a race who thrives off sub-zero temperatures. The DOFF you get from the Rolor Nebula says that the cold depths of space is his home. They have to wear specialized suits that keep their bodies in sort of a cryogenic exposure. Obviously they're smart enough to configure how those suits work and maintain them. Seems like the perfect candidate for an engineer.
Heck, you can even obtain a Borg science officer by running through the middle of an IMR in the KAG STF.... Where's the engineers?
From a game mechanic aspect, yes, the Breen seem to be high-end engineering and scientists, tossing out one well build skill after another (and to my surprise, they seem to use them wisely).
The fact that groups also seem to have at least one engineer and one scientist every time you encounter them further supports your position.
However, both story-wise and canon supports the tactical officer image.
The series was quite clear on, that anyone in the military, was first and foremost a soldier, and everything else secondary.
Even the breen prisoners aboard the Deferi ship support that statement in their dialouge.