The use of attribute and skill tests are for when a task a character is performing poses some kind of challenge. Although humorous, I don't see much of a challenge in walking; quite the contrary as someone who is not very agile would have more of a tendency to compensate by paying attention.
Clumbsiness is not a defect of someone's athletic ability, or lack thereof, but is a lack of attention. If the game includes attributes for dexterity and agility, then the appropriate modifier would have to be given depending on the governing attribute for the task. Catching a football would be a dexterity task (hand-eye coordination), but dodging a tackle would be an agility task.
A degree of clumbsiness could take place due to the ability of an athlete to be more likely to recover from a trip as compared to someone with poor agility skills who is more likely to fall on their face.
The problem with required rolls is that it slows down the game. A better alternative, to me anyway, is to use clumbsiness as a disadvantage, such as in the Hero system. Assign a likelihood of someone tripping over their own feet using a scale as in AD&D's surprise roll (1 in 4, 1 in 6, 1 in 8) and have the gamemaster roll the appropriate die at their discretion as to when. Of course, a good gamemaster would be making random die rolls for no reason at all, just to keep the players nervous and on their toes.