As a cPanel webmail user, you wouldn't have access to the access_log for this at all. You'd need to discuss this with your administrator and they should be able to provide you with the relevant log entries.
As user, I think that compromise your privacy .. because the administrator can show you what he wants. The cliente side log, sould regist every access to the email, and more informatition to keep the confidance of the user.
I think thats shoul be an improvment to the service, and more nowadays, in terms of the privacy concern's.