Edwiser apparently is the Wordpress Moodle SSO plugin but I have not used it personally.
There are many advantages to having logins for a Wordpress/frontend site. I run Joomla and Moodle with SSO - Joomla handles all our event registration and users need to be logged in for that. I also provide the links directly to the Moodle courses from Joomla site and they are only visible to the users that I want to see them.