Re: 250 yards is a respectable carry distance
High handicappers are high handicappers for one reason; their swing. They miss fairways and greens. Look at Vijay Singh. He can barely make a four-foot putt at times, but he still shoots in the mid 70s with those rounds. Johnny Miller, when his putter was so far south it was sitting on an ice cap, and 4 putted multiple greens in a round, still shot in the 70s, or at worst low 80s. These are on the PGA tour, that's still nearly scratch golf.
Short game is what separates a teaching pro from a tour pro, not a high handicapper from a low handicapper. This does have a lot to do with driving distance as well. Miss hitting the center of the clubface regularly, and you're not hitting it anywhere. Forget the marketing hype, clubs are not forgiving enough to let you hit it an inch off center and still get 260 yards, let alone 300. The full swing, in golf, is a lot. Many higher handicappers believe that they can practice chipping and putting all day and become a scratch golfer, and curse their bad short game for their handicap. It's total baloney.
A fundamentally solid full swing begets a good short game. The same fundamentals are used in each swing, even the putter. If you were able to hit every fairway and every green, but three-putted half of the holes, you'd shoot an 81. Most people here would be happy with an 81. That's an 81 with nine three putts. Even the worst putters here would likely not have nine three-putts. Go play a round, and hit one ball as normal, and take another and drop it on the green at the farthest spot from the hole sometime, and call it a green in regulation, then putt it out. I can guarantee that you will score lower with the ball you drop on the green.