The problem for me at least for mobile access is that I do not have my "real" email tied to my phone. I have an Android phone, but have a separate gmail address that is only used in relation to the phone (activation, google play account, etc.)
If I have to read an email in order to sign in to a web app or website on my phone, that means I need to get on my computer and go to fastmail.fm. Which is inconvenient.
Very similar for me. The only emails I get on my iPhone and/or iPad are alerts for $work. For anything else I have to pull up my mail client (I don't use webmail) so it's a huge pain in the ass. I'm hoping this method of "authenticating" quickly dies out.
If I have to read an email in order to sign in to a web app or website on my phone, that means I need to get on my computer and go to fastmail.fm. Which is inconvenient.