Yeah but surely the closer you get the more you close down the angles meaning that you can cut off more? Im sure some pro came out with that statement and I agree.
Then if the batsman feels that he wants to go over the top back your bowler to be good enough to not allow him to be hitting them high risk shots easily. Or a simple in out field counteracts this and not the usual ring fields which are set far too often.
To some extent you are right, a man in closer can cut down more shots. However, this relies on great reflexes from a near stationary position (as you simply don't have time to take more than a half stride either way). I'd even go as far to say an extra 10-15 yards allows you cut off balls you couldn't do normally as you are on the move with the extra time.
In out fields or a staggered inner ring can do both jobs. Say your extra cover is closer in, you can drop your mid-off/cover slightly deeper because the batsman has to pause until the ball clears the short extra. I did something similar in one game, by accident than design, with a extra/point in much closer and the cover/mid-off/backward point deeper. Caused havoc for the batsman as they were never sure of the quick single or the ball beating the field. Helped I had a good bowler bowling at the time. The problem with doing that is when the batsman is happy to hit over the advanced positions or the outfield is lighting quick and the ball needles through the gaps created by staggering. More a ploy for a slow deck where shots aren't timed or go in the air for short distances.