It will aid speed of play, without a doubt. Rather than having to wait for your playing partner to get over to the pin, while you are ready to pull the trigger on your birdie putt, you can go right ahead and get it done. Faster is definitely better for everyone.
From a playing point of view, that flag stick in the hole can act as a back stop for you, particularly on a sloping, downhill, tricky left to right putt. Leaving the flag in will make the hole seem larger and will reduce the fear of running your putt way past. Any contact with the flag stick will slow the ball a treat. Yes, there may be the rare occasion where the ball bounces off the flag stick and stays out of the hole. But in my view, these rare occasions will be more than compensated for by times that the ball will be helped by leaving the flag in.
So in summary, this new rule will help on two fronts – speed and performance. I recommend that you leave the flag in when putting, let it give you more confidence and watch those putts drop.
For more info on this and some of the other rule changes, take a look at this helpful summary from the PGA Tour website.