If it's any help to you...
The Century Class is not a warship. My intention was for it to represent a return to the 'multi-mission' category of Starship, such as the Galaxy Class did 40 years before this class was launcher. (First Galaxy started testing around 2355, this ship commissioned in 2395) First and foremost, the Century Class is an Explorer. The heavy shielding, armor, and weapons are simply required for the ship to be able to execute any and all Starfleet policy options, including defense.
That being said, the Galaxy Class did receive a combat capability upgrade in the 2370's when it became necessary, so I suppose if there were a need for this ship to be upgraded in the early years of the 25th century (hence the name) then it's not inconceivable.
Btw, if anyone's curious, I first got the idea of the name Century Class when I was driving down a freeway and a big rig pulled up along side me. On the side of the engine cover it read "Century Class".