Is this a design fail from Apple?

TLDR; If you have two-factor authentication on, don't have trusted devices and are bad at remembering passwords then don't lose your iPhone.

So a friend of mine just lost his iPhone and tried to find it using Find My iPhone feature from my phone. Only problem he can't remember his password. No big deal we thought. He still has access to his email used with apple id, so we can reset the password through email. Boy we were so naive! he had two-factor authentication on and no other trusted apple devices. Turns out account recovery will take days or more more. This makes "Find my iPhone" useless because no iPhone can last several days without running out of power.

So I guess the take away is, 1. don't use 2-factor authentication 2. If you want to use 2-factor auth then buy more iDevices or don't forget your password or simply don't lose your phone.

I'm sure this is done for protecting iCloud account but at the same time this is a huge inconvenience to the user. Makes me wonder 2-factor auth isn't for everyone.