Here is a great article examining some of the key differences between a classic FPS like DOOM and many of today's shooters. The author makes some very good points, and much of it I had never considered before.
One thing that's bothered me about cover-based shooters from the beginning is lack of "skill" involved. Enemies all have instant hitting weapons and your character moves like cold molasses. So you can't run around and dodge or really use the environment to your advantage. It pretty much boils down to: Duck behind a wall, wait for enemies to expose themselves, poke your head out and fire while absorbing bullets. Duck back and wait for health to regen. Throw in a grenade for good measure.
I'll always have a love for classic "twitch" shooters, even though they seem to be somewhat of a rarity these days. There will always be something fun about dodging fireballs and rockets while trying manage health, armor and ammo for your good guns. I think Painkiller was the last game I played that did a good job of this.