Joomla front-end (
index.php) and back-end (
administrator\index.php) is built as two separate applications, so for security reasons you have separate user sessions and user states. As you noticed, logging in to your back-end does not log you in to the front-end.
There is an extension available at JED called Wow Login that seems to be able to do what you're asking for. I haven't tried it, but according to user feedback it works as expected.
I understand that you want to save your content managers the hassle of logging in twice, but unless it's really important, I would leave it as it is. You can make a small login link in your footer if you don't want to have a login-form at the front-end.
Login tip: I have added a bookmarklet in my browser bar (Chrome) with the following code:
It will show you a login form for ANY Joomla website by adding
&option=com_users&view=login to your current URL. It's a quick way to log in to any Joomla site you manage.