"To solve the problem where the server only transmits stuff once, the replay mod could always listen, and just delete the extra stuff that it didn't need."
That's exactly what the replayeditor does, why not just use it?
Because it can't be done in-game.
For example, if want to start a game of, lets say, skywars and I started in the main lobby, I'd have to load the replay, remember the time of the beginning of the match AND the end of the match (there's no way to automatically cut from a specific time in the video until the end), and then load the (new) file again. It would be easier if I could just join the server, pause it (or even have the ability to pause the video before joining the server?) and resume the recording when starting the game, and pausing once you've won. Would save some time!