Also, other than ranged attack roles and armor class bonus, how often is a straight dex check used? I can load heavy on Tumble and Balance and have a very graceful character with a 7 dexterity.
Not really. You'd have a clumsy character that has learned some skills, with some difficulty. For a real world example - I am not particularly dexterous (I wouldn't put myself at a 7, but I am not rolling in the positive modifier department). I can, however, skate like the wind, due to years of playing street hockey (inline skates, but I can skate on blades, too). Forwards, backwards, transitions, crossovers, anything short of pulling off lutzes and double sow cows. While skating I look pretty dexterous. I use top of the line gear, with the best bearings, built for speed and control. Yet all of that, and I still sometimes fall while standing still on the sidelines. All those skill points, but I'm still a clumsy lug (and a bruising defensemen

). I can't escape my low dex.
As a GM, one thing I do at the start of any campaign is spend some time with the character sheets. I look them over and see what the players spent their resources on, what seems to be important to them, and what impressions I can get from their sheets. I am looking for lots of things - background notes to work into the game, player preferences (if a guy spends a lot of time and space on mundane equipment lists, he wants that to come up in game), and I look at the character with an eye to how others in the game world will perceive him. Stats play a big roll in this. Regardless of developed skills, clumsy is clumsy and socially awkward is socially awkward.
A player has the right to play his character as he sees fit, but his attributes affect how he appears to others. Someone may be a slick lawyer/businessman type, but if they are a snivelling, obsequious worm with a CHA 7 (perhaps James Spader in Wolf), it's going to have an affect on every interaction.
Long and short of it, I think, is that roleplaying is always the great equalizer in "fixing" system shortcomings.