You'd think so, but some how they seem to miss uncloaked ships all the time. Maybe they can't change direction very fast at their speed. Meh.
Partially alleviated in the new star trek movies, but I always wondered why they didn't just shoot the incoming torpedoes out of the 'air' with phasers. Or better yet, blast them right after they came out of the tube so they blew up next to the enemy ship.
Somehow in these shows, it's possible to easily miss targets several feet away, and I believe the phaser rifles have some kind of targeting and aiming system built-in.
(Then there's the wide-beam setting on phasers, which I think they only used once.)
Other random thoughts:
Then you've got the "brilliant" idea of what amounted to a heat-seeking missile in ST6. Why this isn't used more often, or why it wasn't thought of before then...only the writers know.
For firing while cloaked: Use missiles. You don't need any additional power, except perhaps to open a door covering the missile launch tubes.
Multiple power cores: Defiant has a triple-thinged warp core, so that can be done - power the cloak, and power something else.
Finding a ship that's cloaked: Short bursts all over the place, similar to what was done in Nemesis. Enterprise has a lot of phaser banks. Set up a handy little keyboard macro, and start firing short low-intensity phaser bursts all around the ship. As soon as one hits something cloaked, it should be quite easy to keep a lock on it and hammer away at full blast.
So yeah, the "no-firing-while-cloaked" looks like a big plot device, with a lot of simple and unused workarounds, and nothing more. They need an engineer or two on their writing staff, to get some of this sort of thinking. (Or maybe just a few true nerds.)

And think of the savings on special effects budgets. Two cloaked ships, fighting each other using cloaked missiles. Doesn't get much cheaper than that.
It's already been said.
- The power requirements basically take most of the energy output a ship can make to run it.
- Second, you need active sensors to provide weapons guidance. Part of running a cloaking device is similar to how submarines run - as silently and passively as possible. Any energy emissions by the ship even while cloaked will give it away, making it a sitting duck.
The missile solution would be able to take care of these problems. It would be able to propel itself away from the ship, and it could be self-guiding.
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Partially alleviated in the new star trek movies, but I always wondered why they didn't just shoot the incoming torpedoes out of the 'air' with phasers. Or better yet, blast them right after they came out of the tube so they blew up next to the enemy ship.
I liked that the Stargate writers dealt with this, mainly in Atlantis. The Wraith would
immediately start shooting at any incoming missiles, and generally did a pretty good job of intercepting them.