That would require a watch for each player, and the desire to keep track of the time so it does not go over.
The timer does this with a sound, the watch does not.
The timer can account for different time signatures for each turn segment, while the watch cannot.
The hourglass is another stupid idea, because it cant be adjusted for each turn segment and they mainly make only 90 second sand timers or 1.5 minute sand timers.
Buy one timer and move it to the turn segment and press the programmed button and all this time accounting is done by one unit, rather than 6 watches or sand timers that don’t work.