Using that analogy, if the electrician has nothing to do for 5 mins, and the carpenter has a lot of nails to bang in, the electrician should move over and help the carpenter out by banging in a few nails and then when the time comes to do some wiring go and do it, therefor they are acting better as a more effective team.
Seems to me that you are taking the argument to be that Barkley should spend all game chasing the ball down like a headless chicken and arguing against it, rather than the actual point being made.
That point being that every player on the team has to do some defensive work, the whole "thats not their job" defense is daft. It's not a defenders job to score, but they still do. It's not a forwards job to defend, but they still do. It's a players job to help their team to win a game of football, they all have roles to play when it comes to doing so, regardless of what their main role in the team might be.
Barkley needs to defend from the front more than he does. That doesn't mean he needs to be so knackered from doing so he can't create and perform in an attacking role.
He shouldn't be strolling around half arsed when a team are building an attack he should be trying to stop that attack. Not by running around like a headless chicken, but by putting more effort to close down and pressure the players than he does.