It is just unreliable to depend on an external system and external UX to delegate the authentication on its whole. It is the cheapest way of delegate auth I think and has notable flaws. It can work.

1. bad UX, extra email step. Every. Single. Time.

1.1 Sometimes email servers take a while to send/receive emails.

1.2. Constant flood of emails. Swipe to delete might be OK a few times, but at the end it is a user overload.

2. No 2FA as with the process here, if added the process will get real very soon.

3. you still need tokens for the session and prevent someone else steals the key and makes a double login (e.g. looking at someone screen)

4. User might want to change email, so you auth system will need to implement real world UX sooner or later.

5. Think like a business. When problems arise you might want to assist the customer in a personal way. What will happen when their email got compromised? 2FAA to the rescue?