Button make it quicker but why should I close the client and re-open it from Battle.net in case of a disconnect ?I simply enter my password and that's all. Close and Re-Open was never needed.
@ Kyphala: The WoW Client periodically asked for authenticator code again when entering password at the login screen, while the battle.net client can be set to "remember me on this pc" or something like that. So Close/Reopen was usually the faster way.