Umm there needs to be zero distance. You just give the players the adequate headsets. That is all the solution needs to be. Every IEM has done this for a decade and almost every EU LAN has done this for longer.
You can even ghetto out and just get -40dB or -80dB ear muffs and make players use in-ear (which is pretty standard) on stage.
Putting the players further from the audience or removing them completely is a huge drop in quality and will lower your ability to portray the 'storyline' of players and the event(s).
Yet when people have used "noise-cancelling headphones" before, you're still able to hear the droning in the crowd, leading to situations where you can hear when they're cheering / getting excited. For example:
WCS, we had sound-proof booths, noise-cancelling headsets, white noise, in-ear headphones. In game 3 vs Mafia, he was able to hear the crowd cheering when I burrowed my roaches under his army, leading to him checking everywhere for nydus / other sort of weird things.
ACL Melbourne, I had headphones + in-ear, had both cranked to 100% volume (this really ******* hurt my head playing the games) and could still make out what the casters said.
IEM has also had issues with players hearing the casters before, and I wouldn't be surprised if they could hear cheering through the headsets.
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