I'd like to use the two-factor authentification, as you suggest. However, I don't feel comfortable doing so, because I'd be screwed if I lost my phone then.
That risk would be eliminated, if you'd offer backup codes, like most services using 2FA do.
Let me know what you think! :)
Edit: Here's someone that already fell victim to this: https://forum.elysium-project.org/topic/33736-no-login-after-smartphone-crashreset2fa/