> 1. Sending emails is not very secure
Agreed. This is a stopgap measure until there is some agreed-upon standard for 2FA that doesn't involve email or text messages.
> 2. Delegating your authentication to a 3rd party is probably not a very good idea
Again, agree. This is of course assuming that everyone has an email provider of the gmail kind that they are both comfortable with trusting with everything and that it will always be available. That's a pretty bold assumption - but I think it's a pretty common one.
> 3. You still need to use a password somewhere e.g. accessing your emails, it can't be mitigated all the way down
It delegates the problem to a place you can trust, where you use a 2FA app or even a physical key, or at worst, a huge password of the kind you can remember ONE of, but not one per service.
> 4. Increasing the importance of social media accounts / email and allowing walled gardens to act as gatekeepers to services is annoying at best and very harmful at worst if you are concerned about your data
Yes, I realize the irony in trading the security of my data in 100 sites for storing it at google. It's a tradeoff I'm willing to do however, lacking some better solution (such as sites actually switching to using some standardized authentication method with physical tokens or similar).