The only difference between what you're proposing and the new rule is that you don't get rewarded with extra possession time by clearing quickly. With 90 seconds at the start of a possession, if you are able to clear it in 10 seconds, you get an initial 80 seconds of possession time in the offensive end before you need a reset. Under this rule, regardless of how long it takes to clear you still only get 60. I also think they did it this way to make sure the timer operator doesn't make a mistake and not give the proper amount of time. This way it's always set for giving a 60-second countdown and the operator just needs to watch the referees' signals for when to start the timer and reset it.
I probably missed it in the discussions, assuming the timer gets turned off during a penalty as it does now, was there any mention about how it would be handled when the penalty is over? I would imagine the timer would start up again when the penalty is released, but does the team in possession get the full 60 seconds?