I don't even think they need to. If they added message history limits, and maybe capped how many people can use voice at a channel / join a voice channel to Nitro only, they'd likely make a lot of money. Gamers spend good money on good products, but as long as it's all free, they have no incentive to do so.
If they make voice chat require nitro, it would most likely kill the product extremely fast (my guess would be that people move to Steam, but there are other options as well). For things that voice chat is generally used (usually some kind of team based game), vast majority of people definitely don't want to limit their team mate pool to people with Nitro subscription.
Requiring certain number of nitro boosts might not be as serious, but that would likely just make people consolidate servers more (possibly split text and voice servers, but at that point they might as well consider other options for voice).
I think there is probably room for discord to sell 'premium' voice channels. Currently their stuff works /most/ of the time but is unreliable enough that a lot of people still use stuff like mumble/teamspeak.
