It won't. Most people don't care about privacy or FOSS. I've been trying to get my friends to switch to something else for years, and they couldn't care less.
ID verification is the least of my worries, to be honest. I've been on the internet long enough to acknowledge a need for something like that. I'm uncomfortable with the fact that data is a valuable commodity now. Discord is storing my online habits and conversations somewhere on their servers. Deleting that information is deleting money.
If people weren't worried about that before, then they certainly won't care now.
You're quite wrong in your assumptions. Most Discord users are moving away from the platform. Fluxer is gaining traction very quickly.