If the warship is to be "dedicated" to something, as in, some of its capabilities are going to be removed because this somehow makes it better at what it does, then logically Starfleet should pare down the ships to the utmost. There would be no "generic warship" because that by definition would be inferior to a "dedicated" vessel that has fewer capabilities.
So we would be seeing dedicated capital ship killers, dedicated small craft hunters, dedicated commerce raiders, dedicated space station attack ships, dedicated planetary bombardment ships, ships dedicated for use against Klingons, ships dedicated for use against the Breen, ships dedicated for use at impulse speeds or against cloaked vessels...
In most navies of today or yesterday, we don't see quite this much diversity because it would be hellishly expensive to build. But suppose money is not a factor for Starfleet. Shouldn't they go for this kind of logic? Too bad that while we do see a great number of designs, they all seem to play more or less the same role.
Alternately it may be that the more bells and whistles a ship has, the better it is at everything it does. Possibly a warship with laboratories and kindergartens would fare better in battle than a warship without (quicker at finding out the enemy's weak spots, has a more rested crew). Even the Defiant's deadliness might stem from the fact that she is crammed full of highest possible tech, not from the fact that she would somehow be a "barebones" vessel.
My take on a dedicated Trek warship would probably be some sort of an austere, expendable platform that has enough oomph to take down an enemy capital ship in one suicidal sortie. Klingons would love to fly one into battle; Feds would probably automate theirs. General purpose starships could handle those battles where self-survival is of interest: fleet battles and planetary sieges would be decided on the mass expenditure of suicide ships against the enemy's far more precious capital units.
Timo Saloniemi