As the bracket progresses, there are less matches each round. This leaves vertical space between each match. For example, in [winners] round 3, the vertical space between each match is three times the height of each match.
In tournaments I am involved with, the bracket is displayed on a projector. Due to this vertical space, the bracket has to be shrunk so that all the matches can fit on the projector screen. During early rounds, this is of little importance, but as the tournament progresses, it is important that the matches can be easily seen. Hiding completed rounds would allow for the bracket to increase in size as the tournament progresses.
If completed rounds could be hidden, then the bracket could be redrawn with reduced vertical space between each match. This could either be an automatic setting, or done in the menu accessed by clicking the round label.
Additionally, for double elimination brackets, the loser's bracket has twice as many rounds (less four) as the winners bracket. For large tournaments, the losers final is far to the right of the grand final. If completed rounds could be hidden, then the losers bracket would better synchronise with the winners bracket as the tournament progresses.
As an added bonus, it has an added bonus in sessions split into multiple sessions. For example, if a tournament starts on Saturday with 256 participants and ends that night once 32 participants remain. The reduced bracket showing only the rounds with the remaining 32 participants can be published that evening so everyone can see the bracket before the tournament resumes on Sunday.