Ships of the size for just transport sounds reasonable but considering that space is devoide of matter, ship speed would be irrelivent.
This is where you went wrong. A ship's speed isn't that important, but a ship's maneuverability IS.
No ship can avoid a good laser, but if you can place your ship somewhere outside the kill zone before lead can reach your location, then you won't be easy to kill.
Also, some guns don't turn very well. A large ship with a spinal mounted gun can never maneuver to hit a fighter. Bigger guns usually means slower turrets, or at least you'd have to sacrifice turret armor to bring it up to speed. Both situations favor the utility of a small fighter craft, and the bombers that would feast on such targets.
The main appeal of a figher would be the ability to get in and out of firing range(or a firing arc) very quickly. Big guns will turn them into space dust, but that won't matter if the guns can't secure a firing solution in time.
For one possible scenario, you're patrolling around in your big ship, taking an encrypted route. The enemy has decrypted the route. They launch fighers from a week's distance away, spending two days accelerating towards your location. They're running cold after that, are tiny, and are nearly impossible to pick up on sensors if they're more than 20 mins away (except with their catapaulted speed you have 3 mins). A minute before before contact, they release their payload, and zip by you never to be caught. Forget shooting them, you have to keep your ship from blowing up! You had a 2 week window on patrol to be attacked, and out of that you had to be ready for an attack that would only last 5 minutes! Good luck making it to the bridge in time to get briefed. It's kind of an extreme scenario, but you definitely couldn't do that with a big ship!