The issue is that with Wild Shape, your physical stats are replaced by the wild shape's stats, unless your own would be higher. It's designed for druids to be able to take advantage of increased stats via wild shape.
I personally don't know any druids who have used wild shape to get around carrying capacity specifically, but I have seen them use wild shape to get a high strength to let them do more than they would normally. (eg high level druid using earth elemental to shift a very heavy item, that kind of thing)
