Have you considered not requiring email at all? Those are my favorite sites. Your site provides some good or service, I just want that from you. But if I do, chances are I and younger people in general don't prefer email since there are a myriad of other options.

Whether or not I am a member of amazon is a very serious privacy issue for me depending on who sees that information and correlates it with other info.

For security, this terrible lazy way of relying on email causes a lot of problems for users. Access to your site should not depend on a central point of failure: users' email. Believe me when I say getting your email pwned is made even more horrible by the fact that random accounts are now also compromised. Doesn't matter if you use a password manager. If you use 2fa, you have to have some means of reseting accounts other than email, else you're just federating to email.

If you just want to federate thr real authentication to their email provider them use Oauth2 with Google, Github, Facebook and Microsoft. Let them do auth but don't require email.

At this rate email will outlive ipv4! Lol