I think it's fun to play more than once to challenge myself to improve.  I agree that it's a personal thing.  There's no right way to play.

Y'all are welcome to play the way you choose to play. Some of us try to find lower moves after we play the first time.

 Sounds good to me -- that's the way I play.  

I play the game until I finish it once and then don't play any additional times. In my humble opinion the first time one completes game should be the moves and speed that counts. Not after playing it 10 to 15 times like many players. Of course, each subsequent time one plays the game their score and speed should improve. Practice makes perfect after all. It's akin to taking multiple mulligans in golf. I've personally been playing the game this way for the past 12 years or more.