If you run Windows Store Apps you will need to run the modern interface. Windows Store Apps do not run in the Desktop. You can see them in the task bar and pin a shortcut to them but they actually run in the modern interface. It's still two headed, though not as confusingly so.
The Windows Store has you sign up for an account, in the same way Apple's App Store does. That's why you sign in with it, it wouldn't make any sense to sign into the store with an account that is local to your computer.