I think "Reachability" is the only real
problem for the whole thing. Everything else can be solved.
(Email should always be an option for account creation.)
For example my current VPN provider is very privacy focused and allows account creation with just a username (maximum Accessability) and offers quite anonymous payments using Monero and such. (They used to allow cash via physical mail as well but it had too much administrative overhead for the number of users and might be illegal in some regions.)
Recoverability is obviously an issue here, but that can be solved in a similar way to your backup for 2FA methods. Just have a set of single use codes to recover your account. Of course you could lose those as well, but users who are so privacy conscious that they opt out of using email would usually be organized enough to keep such backup codes in a safe place, like a password vault or do some fancy cryptography stuff with it for fun. Otherwise they might just not care and accept they might lose this account. Alternatively this could be solved with an authenticator app or a physical security key/token. Each of them have advantages and drawbacks, but all have open standards and can be used in various ways, so letting users choose one or even multiple of these options should provide good accessibility and recoverability.
Then the only issue remaining is "Reachability". How this is handled depends on the reasons why it might be needed. If this is about ToS and the option to issue warnings for example, it could be solved by simply making users accept that if they do not provide their email, any breaking of the rules will lead to an immediate permanent ban.
I can't come up with any other reasons than that and recovery, why users might need to be reachable outside of the platform. Anything else (except maybe announcing a shutdown of the site) could be handled by a message on login.