Normally the user would enter text and hit [Enter]. With current placement the user may need to enter the text, then click the provider button, and click [Sign in]. If we put the provider button in front of the whole box, then then prior to entering the id user would choose the provider (it also should be smartly preselected, e.g. from a cookie).
There fore instead of the sequence:
- Enter text
- Click, Click - to choose the provider (optional)
- Click (or [Enter]) - to sign in
We'd have:
- Click, Click - to choose the provider (optional)
- Enter text
- [Enter] (or Click) - to sign in
The second behavior looks faster and more natural.