It's no different than using Skype or Ventrilo or even a phone/conference call. There's no real way to manage who talks to who while you're playing a game.

In my experience most games with in-game voice chat don't turn it off when you're dead anyway so it wouldn't matter.

Honestly, no. What you are talking about is known as "ghosting" and games where that's an issue there is usually some way to limit "spectator" mode or put the viewing of what's happening in the game on delay. For everything else, it's just expected / wanted to have continuous voice communication.

There's nothing in discord that Valve hasn't had built-in to steam or other applications have been doing for years.

Voice apps for games have been used for a long, long, long time. Most games don't really keep a constant voice connection (it drops during menus), and it can be very hard to coordinate to all be on voice together in a multiplayer game. Plus a clan may well be too large to fit in a single "squad" or "team" in a game, and require multiple levels of coordination.

Coordination isn't cheating.

If this is an issue than you solve it by not allowing members of the same team to view an opposing teams views.

Not allowing external voice chat is a horrible idea.

The general way this gets solved is to disallow dead players from seeing anything that alive players cannot see. This is how popular games like CounterStrike work, even with the in-game chat.

An old anecdote...

Back in the day, in SOCOM 2 for the PS2 (5v5 slow paced shooter), there were "alive" and "dead" chats for the players on each team. The dead players could look at alive players in the 3rd person, but pan the camera to always watch their back instead of what they were typically watching.

Dead Players found that they might spot something that alive players didn't notice behind them, so one of the dead men would go into the menu and vote to kick the alive player. The alive player then saw this notification, and knew to check their back.

So future games made sure dead people's POV cameras === alive players, ideally. Then dead people can talk and there's no trouble with messaging or skyping outside the game or anything.

On more competitive CS:GO servers the built in voice chat is intentionally disabled between living and dead players not to prevent such "ghosting" (which is just part of the game) but so that dead players can chat without disrupting living players on their third party (TeamSpeak, Mumble, Discord, etc.) voice channel.