Plaintext email could be stored client side in a cookie and may be submitted to the server when use of the email is required, and if it validates.
If the user logs in and the site is down, a backup system could email them about the issue. This is the backup system, primary systems are down. Please contact support if you need more information. No need to email users who aren't using the system currently about downtime, or in fact no need to email users if they aren't using the system.
Further, if a "password recovery" flow is modified slightly, it can be repurposed for password-less logins by using strong tokens sent to user email, as they request them. A simplified 2FA flow can be established as well, where a token is texted the user after verifying email address. A second layer of security to texting tokens can be achieved using Google Authenticator.
To use such a system, the user will need to be OK with sending their email address each time they need email from the system AND be OK with having their phone handy to login. Of course not every use case requires security, or can be used with this proposed security system.