First, I don’t want to eliminate Session use for logged in users. But I think my website is poorly designed if having a non-member block cookies will screw up how my error handler works. (Thumbs down for me!) 
As to your comments above, I don’t think we understand one another.
Let me explain again…
First, I have a script called “errors.php” which is in change of displaying a customized error page for every error in my website.
When a given script (e.g. update-email.php) has some error (e.g. “Email not found in database”), then it places the Error Code in $_SESSION and redirects to “errors.php” which then finds the corresponding Error Code and displays my Error Page template with the appropriate HTML.
Follow?
It seemed like a good idea when I created it years ago. However, the problem that I discovered last weekend is that if a user blocks cookies, then $_SESSION[‘error_code’] is always NULL and so “errors.php” always defaults to a generic catchall error since it can’t figure out what the Error Code is?!
That was a gigantic miscalculation on my behalf!! 
In another thread on SP, I am trying to learn how to use JavaScript to check if the user blocked cookies, but even if I learn how to do that, it still doesn’t leave me much of an option because if cookies are blocked then it breaks my error-handling.
I am hoping that there are some ways I could re-architect my website going forward so that I am not dependent on Cookies or Sessions to display errors or my customized error page.
Now, by contrast, if a user is a member, and he/she blocks cookies and then can’t log in, well tough for them. But for visitors, it seems rather self-righteous on my part to demand they enable cookies just to surf my website!!
(When other websites demand that I enable cookies to surf their site I just leave!!)
Does that make more sense?
Nah, I don’t like that for security reasons and aesthetics.