Does the home page need to be a front page menu item?

From Joomla! Documentation

The "J1.5" namespace is an archived namespace. This page contains information for a Joomla! version which is no longer supported. It exists only as a historical reference, it will not be improved and its content may be incomplete and/or contain broken links.

No. In Joomla! 1.5 and newer, the home page can be almost any type of menu item and can have any name. The only requirement is that one menu item must be assigned as the "Default" menu item. This is the menu item that will display when a user navigates to your URL.

Also, any menu item can be assigned to use the "Front Page" menu item type.