In that case, is a YouTuber liable for the GDPR failings of Google? Of course they aren't. It's the same here.
Is McDonald's liable for the GDPR failings of X? They have an account with their name and brand on it. They even pay X for a golden checkmark.
Is Taylor Swift or UGM liable for the GDPR failings of Spotify?
Are individual eBay sellers liable for the GDPR failings of eBay.
I could go on, but you don't quite seem to realise what the implications of what you're saying are if they are true. You're basically making every user liable for any GDPR on any service that collects any data. This isn't the case, or businesses wouldn't use these services.
How else is the platform owner to prove that the account is linked to an actual person without defeating the check being trivial? They can't without something being tied to you. An email address may have been a good one to use back when AOL gave out addresses as part of their subscription service, but the availability of free email has destroyed this possibility. Out of the many things that could be asked for you to provide, a phone number is the least nefarious.
You reserve the right to not give your phone number to Discord. You do not need to give Discord your number in order for you to be able to use it. Likewise, the server owner reserves the right to ask Discord to only allow accounts that have been verified to not be burner accounts. Email verification does not do this, and the time limits on membership only go as far as slowing down accounts used in bad faith in a server, whether that be scams, trolling or otherwise.
Like many things in life, it's a trade-off. You value your right to privacy more than being granted access to this particular server. The server owner values the reduced ability of trolls and bad actors over the loss of membership from users like you. Unfortunately you cannot have your cake and eat it too.
The only alternative I can think of is just buying a pre-paid number and a cheap second hand phone and using that only to verify with services. It's good for 2FA too as it makes you immune to SIM swap attacks.