I completely agree with the points made by @hugollm and @maruru. Make sure the user is aware of how the system works, and do keep in mind all the steps that may make it harder for certain users.
Thus, I don't think that this system should replace password logins completely because it's great in certain cases (especially mobile) but in others you really prefer to just type in a password or have a password manager do an auto login. I like how sites like Medium and Slack offer password-less logins but don't completely use it to replace their password login system.
From personal experience, I love using password-less login for Slack on my phone. Whenever I am adding a new account, it offers to send a "magic link" to my email and since I already get notifications on my phone, I just open the email and click the link. If for some reason I don't have email setup or am having issues, I can just type the password as usual.