Most sites that implement it this way do indeed have something similar to what you describe for Microsoft. e.g. many sites these days allow for "magic link" lo

Most sites that implement it this way do indeed have something similar to what you describe for Microsoft. e.g. many sites these days allow for "magic link" login where you just enter your email and they send a link to login. There is no password to login with. The problem from there is that users are dumb. If you have multiple login methods, many users will not remember which method they used to login last time. So if you show them (by default) a username/password form, they will try to "remember" a password that might not exist if they used any method that was not username/password. Much better for that user if you make them enter their email, you do a quick lookup in the backend to determine which method they used to login last time, then you proceed with that method in the frontend.