Your little ships are visible from beyond their own tactical range and get shot down before they do much good. They are too small to carry effective defenses. I'm sure the a small craft like a fighter would need hefty hardware to power a shield strong enough to protect against a full sized capitol ship's phasers or what-have-you. And to top it off, your sending real life people in these eggshells to get fried.
Star Trek is a little different because fuel consumption never seems to be an issue, but if it were, you have to carry enough gas to get you to the fight and get you back (assuming you like you pilots) which is double what you might need if you sent a drone out there.
As I mentioned several times earlier in the thread, all fighters would likely be launched from a carrier ship. This carrier ship would likely be very near to the battle, possibly even a participant in the battle (and a heavily armored target to draw away enemy fire). The fighters themselves wouldn't need to traverse across space alone, they would have constant back-up. In fact, most other science fiction depicting space battles has this paradigm.
Star Wars features Star Destroyers and the Death Star, from which the Tie fighters are launched. Battlestar Galactica features Battlestars, from which Vipers are launched. Starship Troopers even takes this a step further with infantry. Starcraft features Carriers that launch ships.
The reason Trek used capital ships and the battles were short is (surprise) they are insanely expensive to film. It's easier to show the bridges of two ships and have the captains duke it out over words than it is to launch several dozen fighters. Even the battles in DS9 were repetitive, even to the point of reusing footage. Over time, that became the style of Trek, and so even today they're reluctant to change that model.