How is it that the NPCs are able to utilize cover based shooting mechanics from games like Uncharted, Max Payne, and Gears of War while the player character can't?

This seems like a huge oversight and really needs to be either patched or modded into the game. I certainly feel that it would also make playing in third person exponentially better.

The animations already exist in the game so I don't know if the devs ran out of time, but it seems like it could have been done by adding a contextual button press behind cover.

Another thing that the game is sorely lacking is the "Run and Gun" perk from New Vegas that allows increased movement speed while aiming any "pistol" type weapon.

Am I the only one who feels this way?

When you are up against a wall or cornor, press the aim button and you will lean around the cornor. The mechanic is actually in the game, it's just not very well explained. I just discovered it by chance.

Well there is a cover system, just not with any animations.

1st person view + close to wall = use of cover.

It's not the same, and you can't even do it in third person. If you're crouching behind something you can't decide if you want to blind fire from the side or pop out on top and take a few shots in first person.