Generally, speaking for myself, Tee box, and fairway shots usually take the least amount of time. Putting, is another aspect of this game. Personally in my opinion, it is one of the most important aspects. They say, drive for show, putt for dough. Hence, I do take the time on the putting green. Depending on the length of putt, etc, etc. So, why rush.
I think putting in a faster shot timer can cause undue pressure on an individual to play quicker, but necessarily better. Most likely the player will not shoot his/her regular game.
That is one of the reasons why I don't play multi-player games, because of my slow play.
Addendum:
Why not have a variable shot timer: For example
Tee Box: 30 seconds
Fairway: 60 seconds
Green: Default 90 seconds;
But as for default across the board, in a multi-player round, it gives you time to relax between shots. Don't forget, this game does require alot of concentration. Secondly, you can rush out make a coffee between shots, or grab a glass of water.