So there are two complaints about this authn scheme that I'm seeing in this thread:
1. It's pretty phishable. I think this is mostly solved, or at least greatly mitigated, by using a Slack-style magic sign-in link instead of a code that you have the user manually enter into the trusted UI. A phisher would have to get the user to copy-paste the URL from the email into their UI, instead of clicking the link or copy-pasting it into the address bar. That's an unusual enough action that most users probably won't default to doing it (and you could improve this by not showing the URL in HTML email, instead having users click an image, but that might cause usability problems). It's not quite fully unphishable, but it seems about as close as you can get without completely hiding the authentication secret from the user, which is what passkeys, Yubikeys, etc., do. I'd love to see the future where passkeys are the only way to log into most websites, but I think websites are reluctant to go there as long as the ecosystem is relatively immature.
2. It's not true multi-factor authn because an attacker only needs to compromise one thing (your inbox) to hijack your account. I have two objections to this argument:
a. This is already the case as long as you have an email-based password reset flow, which most consumer-facing websites are unwilling to go without. (Password reset emails are a bit less vulnerable to phishing because a user who didn't request one is more likely to be suspicious when one shows up in their inbox, but see point 1.)
b. True multi-factor authn for ordinary consumer websites never really worked, and especially doesn't work in the age of password managers. As long as those exist, anyone who possesses and is logged into the user's phone or laptop (the usual prerequisites for a possession-based second factor) can also get their password. Most websites should not be in the business of trying to use knowledge-based authentication on their users, because they can't know whether the secret really came from the user's memory or was instead stored somewhere, the latter case is far more common in practice, and only in the former case is it truly knowledge-based. Websites should instead authenticate only the device, and delegate to the device's own authentication system (which includes physical possession and likely also a lock secret and/or biometric) the task of authenticating the user in a secure multi-factor way.