That's how I run D&D. The dice are there for situations where the chance and/or consequence of failure is significant.
I don't use rolling for puzzles, riddles or talking. If the dragon asks you a riddle, you don't get to roll your Int check to solve the riddle. I ask a real riddle, and then you really solve it. Your wizard might have a really high INT, but if you stink at solving riddles then so does he. Likewise, if you can't talk your way out of a traffic ticket then neither can your rogue. Sorry, but the game is about talking and thinking, and if you want to be good at the game you have to get good at those real life skills.
What if the player stinks at riddles or puzzles but wants to play a character that doesn't - they just can't (this is a legitimate answer at some tables, I'm just checking)? But doesn't this heavily discourage players from going outside their comfort zone?
On the flipside - what about the player that can smooth or fast-talk just about anything. What's to prevent him taking average stats and little skill in diplomacy and still dominating the diplomatic arena?
or the guy who's brilliant at riddles and puzzles but takes low int characters (yet still solves all the riddles and puzzles). Are all his characters just assumed to be idiot-savants?
Just like if your fighter is really smart and is supposed to be a master of small unit tactics, but you're too dense to ever flank the enemy or stage a competent ambush. You don't get to make a "Tactics" roll to have the DM tell you where you should move your fighter, so you don't get to make rolls to fake your way past other forms of intelligent play, either.
What about new players? They can't always be good from the get go. At the very least, I allow input from other players until the player feels comfortable in his role.