I always remember Tom Scott saying "Don't store passwords yourself if you can all avoid it" [2] and how you should leverage google, facebook and other 3rd party authentication methods as a way to add a layer of security and remove one way to compromise your user data.
Some folks i met strongly believe that using a different medium while interacting with a site distracts new users, by this lowering the sign-up rate. I have no data on that but it sounded at least plausible.
If you believe in this, it would depend on your target group how you should handle passwords (or the lack of).
But I want also say that for a great variety of solutions having 2FA or passwordless as default is valid, Slack for example has an option of demanding 2FA for all team members, which a lot of people would agree is a good thing.
The "Password Security Guide" section at the article is a good example of educating people how insecure storing password, and you could do the same thing showing/enabling passwordless as a clear and easy alternative to migrate to.
A system that addresses this drawback is SAW [1, 2]; it splits a token in half (via XOR) and sends part of it to the user as a cookie, and part to the user's email address. Clicking the link combines the two and submits them both to the server for validation.
[1] http://isrl.byu.edu/pubs/pp1001.pdf (short) [2] http://isrl.byu.edu/pubs/saw.pdf (long)
(Yes, that's a joke :p)