It's because your right thumb falls off if you attempt to look around as much if you were playing with a mouse.
It's all sensitivity issues.
If you set it too high, you can check your flanks but not aim.
If it's too low then you can aim accurately, but looking around is impossible.
Being in the middle makes your jack of all trades, master of none

Bingo. It's seriously not even that bad. PC shooters are fundamentally different in that they cater to the gamer's ability to constantly swivel around. The stick is not versatile enough to support the kind of play you are referring to. Once you play a lot it becomes a non-issue, as nobody else has the ability either. It seems like it would be disadvantageous, but that's how console shooters have always been. What would be nice is if FOV on consoles was always 90 degrees instead of 60 degrees. While you can't swivel as nicely, it would provide an added sense of awareness which would be nice.
In a strange way I actually prefer it. It's hard to explain. Like, whenever I play counter-strike or something I get raqed for a good 20 minutes before I adjust my play style to what you're talking about. If a mouse has superior aiming, then a controller has superior movement/action. The stick may not be as good as a mouse, and even though some PC gamers may argue, I can definitely perform more button-based actions than somebody with a keyboard.
If you think of a game like Halo, which has a lot of emphasis on quick jumping and crouching, buttons and left-stick movement are just better.
When I was watching the videos, and it took me quite few to start realizing, it's just something I picked up on. There were times players were getting their flanks wrecked, and if they had only took the time to check, they may have had a chance.
As far as the buttons go between a controller and keyboard, yes, I could argue this lol, and don't forget that not all mice are created with two buttons

Coming from a player who has played a lot of tactical shooters, neglecting flanks and corners on a regular basis is a fundamental blunder. I'm aware that Crysis is not a traditional tactical shooter, but from the looks of how the nanosuit functions, the suit itself leaves an absolute ton of room for tactical gameplay, which I'm looking forward to playing with. I've never played Crysis 1 and I'm sorry to hear that there are some original players who frown on the decisions that Crytek has made in respect to the new changes, but this game looks amazing.
One more thing that just made me cringe in the videos: Players randomly throwing grenades! As if it the burden of its weight was too much and must be thrown in a random direction as quickly as possible.
Doesn't the grenade have its own slot? I hope so!
Take an example from this guy. He is civil.