I am a winning cash game player and have been playing the cash games for over 25 years. I always look at my hand right away, and have noticed that most players do the same. The reason for this is because if I and every other player at the table look at their cards in turn, then the game will slow down to a crawl... This is not good for the game.
There are plenty of times that I have looked at my hand right away on the button and discovered AA, KK, AK, etc. I always do the exact same thing with my hands and posture regardless of whether I have AA or 72. The players in front of me call and raise without a clue to what I am holding.
If you look at your cards early and focus on always doing the same thing, then you won't be giving away any tells. I also think that by looking at your cards when everyone else is looking at their cards, then if you do happen to have a tell - it is harder for them to pick up on it since they are busy looking at their own cards. By waiting for your turn, you give everyone at the table a chance to look at you when you look at your cards. Is that really in your best interest?
So, I suggest that it is in the best interest of each player to look at their cards before it is their turn to act, and it is also in the best interest of the game since it will speed the game along and you will get more hands per hour - which is also in your best interest if you are a winning player.