With single device - you're right... but this becomes really a problem when you expect your customers to use multiple devices: computers at home, at work, smartphone, iPad...
how would you suggest your customer which login to use the first time she tries to sign in on another device?
Would that be my personal email account, my gmail account, my other gmail account, my university/alumni address, my work email or the other work email?
how would you suggest your customer which login to use the first time she tries to sign in on another device?