Fairly obvious that they flag your account in their database. They can't use TLS supercookies for the primary reason that all of their traffic is proxied through Cloudflare - every API call, CDN image, and websocket event.
What's your solution?
In short, no, the alternative is not "being overrun by spam".
You could join mine with almost nothing verified.
Discord sometimes flags your whole account to require a phone number.
It's not a "server"[sic]-specific requirement that can be disabled somewhere; it's an account-wide requirement that cannot be disabled unless you open a support ticket and pray that the person in charge of your ticket is not having a bad day.
I might have gotten unlucky with my ISP, but Discord blocking me from doing anything at all unless I give them my phone number, is what made me leave it once and for all.
Oh but without deleting my account, because I can't delete the account unless I give them my phone number.