There's a catch here: it could trigger a psychological effect, and a player might decide that since it's their timer ticking, they can use it however they want, and someone might deliberately waste time, spending half an hour thinking about each move in every battle. And if before, it was possible to somehow influence this (by talking to the judges or the community), now it will be on completely legitimate grounds: "Leave me alone, my timer is ticking. I'll use it however I want!"
What I'm getting at is that this could have the opposite effect: instead of the original goal – saving time in battle – we might end up with all battles, even the simplest ones, being drawn out.

Do we need to take that risk? Cases where people deliberately prolonged battles and spent an hour thinking about each move are rare in the Heroes community.