2 minutes is plenty of time to think over your moves with all the animations and extra timers added on each action. Sure having more time on a critical turn can be nice, but not at the cost of dragging the game length out by <Dode can probably insert the average game length with 2 minute turns vs 3 minute turns here>.
I don't normally take Open Ladder data, but I took a sample of the past month of play to compare it with Champion Ladder in order to answer your question
The mean length of a match which is played to completion in Champion Ladder is 74.47 minutes; the median is 73.3 minutes.
The mean length of a match which is played to completion in Open Ladder is 73.19 minutes; the median is 72.91 minutes.
Your completed 3 minute matches are, on average, being dragged out by an extra 1 minute and 17 seconds by having 3-minute turn lengths.
To help visualise the difference between the divisions, I put the completed matches into 5-minute bins to produce the following histogram (expressed as percentage of completed games due to the difference in the number of games played total):
higher variance in the longer turns, meaning your 3-minute match is more likely to be either longer or shorter
than a 2-minute match, but on average the difference is not much at all.