Third party apps don't have to use e-mail for logins. They can use user names.
Backers of e-mail based sign-in often call it a "frictionless" method for the users to sign up. What it really is, is a frictionless method for them to collect information about their users.
But this is also specific to "social" logins - eg ones where you aren't intentionally providing your email address.
More in-depth article about it: https://www.troyhunt.com/im-sorry-but-your-email-address-is-...
For accounts that really matter (not throwaways), someone needs to know a fair bit about the user's identity to ensure recovery works. It can be delegated (and probably should be), but that moves the identity problem rather than eliminating it.
Maybe someday we'll all have two Yubikeys (one for backup) and register with each website using them, but that's not how things work today for most users.
This "problem" has been routinely solved by free forum software and other systems for decades now.
(I still don't. My email address is public. But some people apparently do.)
- financial accounts: they would never use a third party login anyway.
- social accounts: None of them are going to let you login with third party accounts anyway.
- work accounts: Again they arent going to use social media accounts. They are going to use some type of ADFS federated account.
- My AWS account: I use Google Authenticator for that.
I lost my original Reddit account because I never gave them my email address and it was hacked. (Using a throwaway password set back when I didn't care about Reddit.) I contacted support and they shut it down, but without some other way of knowing it belonged to me, wouldn't give me my account back.