I've played golf games as far back as bandai challenge pebble beach on the NES, and this game's putting is one of the worst implemented i've seen. 2 quick things would fix it:
1) Tap-ins. The display, golfer, grid, power meter, all aren't designed for putts under 2 feet. It's a jumbled mess. If you get within 24 inches, make the game give you the put.
2) Swing meter enhancment - In every good golf game i've ever played, you don't have to measure a backswing on putting. Reading the break, power, line are enough. On putting, the game should let you set the power, then just let it go and shoot, assuming that you hit the ball 'true'.
4-putting because you can't even see the hole through all the clutter on the screen, or because you read the line perfectly but clicked the mouse too late, are extremely frustrating, and not marks of a 'fun' game.