The idea that tournament matches won't be timed is not open for debate for any event occurring at a large convention, at least in North America. Due to constraints of space and logistics timed matches are the only possible option.
As for timing phases. I do not see forcing people to play faster than they're comfortable with being an option. Time limits are outside a judges control as stated earlier. However a judge has an obligation to make an event as welcoming to ALL players as possible. Limiting time phases penalizes new players as well as individuals who just play a little slower than average for whatever reason.
If we accept the fact that time will always be an issue, why is that not even a bigger reason to introduce time-based phases? From my perspective the more actions that are being played in a game, the easier it's to see who's playing better and who is more likely to win.
Will time-based phases be a disaster for the competitive community? I wouldn't think so at all, I think it would introduce a wider variety of books resulting in a more developed meta. Would this change not be for everyone? Probably, it will require both more deck design and game knowledge but also produce them as a result.
I think every mage wars competitive match should end up with a winner or a loser, preferably by killing the other mage. With more actions, it should be an easier task to accomplish but in case no one dies, perhaps the judge would step in and call a winner. Since the judge has seen the match, both decks and can, therefore, make an educated guess about who would win if the game went on further.
You would only have Winners or Losers, making scoring a lot easier.