It's because they can't fight without their precious constant buff builds. If their buff runs out they actually have to play the game again instead of letting the buff carry them, and that 30 seconds is enough time to lose the buff.

Or if you want to save points to do a mass buy it could cut down on run time overall.

50 rounds, it's like 10 seconds between rounds, so barely over 8 minutes of extra time on a run is added from the timers. And if they added in a voting system, you know Bungie would make it some awful one-sided "majority" thing, so if a player needs extra time to double check something, or is debating whether to save or not, or even just deciding whether to upgrade one tower or another, and the other two decide "-blam!-'em", you're screwed. The insignificant wait time between rounds is not severe enough to warrant adding a feature that would 100% be used to ruin entire runs for people.

If implemented as everyone has to opt in to skip then issues can be avoided. The wait time affects shorter runs more than long runs due to the lower need for defenses and that farming 5 10 wave rounds goes faster than 1 50 wave round. So those 30 seconds add up if you are farming.

Do you really think Bungie would ever make it an everyone-has-to-opt-in thing?