Doge, I'm also not sure what your issue is with the golfer who needed a cart. From what I remember, he had a genetic deformity that resulted in him being unable to walk the length of a golf course. He could still swing a club though. The cart allowed him to complete a round. It really didn't, IMO, give him any real advantage - and the results showed it.
If pros also had to carry their own bags, which would make the walking more difficult, then yeah, I would agree the cart would have given him an unfair advantage.