If you uncheck "allow all computers...." then you may indeed have problems with users not being able to send email. Microsoft recommends that you always leave this checked, and if you test your system with it checked, you will see that it does not create an open relay by having this checkbox active.
Yes, you want to limit the scope on your "only the list" list to any internal computer or device that needs to relay email without authentication. This would include things like scanner/printers that have the capability to send email through your SMTP server or software that sends email alerts or messages automatically without using a user name/password to authenticate with your server.