There should be a configuration available through "Confluence Admin" that sets the "Remember me" checkbox on the login page to be checked by default.

Though I don't have any suggestions to offer regarding the current UI, I find that most users aren't really aware of the checkbox, nor do they investigate it. They just skip over it directly to "Log In". Most of these users instead choose to have their web browser remember the password - which is less secure, as it requires the web browser to remember the password, instead of just a cookie that stores the Confluence session ID - from which the password cannot be retrieved.

I'm including a patch for login.vm that can be used to change the checkbox to be checked by default. This is not an ideal work-around, as the patch will need to be re-applied with any upgrade to Confluence.