cannot change priveleges

I am not sure when you did this, but you should never (even in previous versions) change the permissions of your system drive. Ultimately this could have led to your mac failing to boot, or you losing access to the contents of the drive.

In Catalina and Big Sur, it is forbidden to modify the contents of the top level of the drive, and that is with good reason.

Well, actually in Big Sur you cannot possibly do it, because that part is mounted as read-only; so even if you were root, you couldn't make changes.

Let me reiterate: this is a good thing. It preserves the system and prevents unwanted tampering, as well as dangerous user error.

You should not have to boot into Safe Mode to be able to change the icon.

This suggests to me that you have installed stuff that may be blocking this (and probably other things).

Without knowing any more details, I am guessing that you may have some third party "antivirus".

There should not be one.

Effective defenses against malware and other threats

James Roberston wrote:

No that does not work. I am locked out of the icon.

I don't know why that is not working.

Here is my main drive with a picture of Daffy Duck 😎:

That is perfectly normal. You do not own the whole drive, system does. You cannot change that.

I am not sure about the icon, though.

Replying to myself... you can change the icon, too.

Just copy the desired one, then select the icon in the Info window and Paste.

Aside to your issue but might be related. Big Sur is now up to Version 11.5.1 versus quoted 11.4. Be sure to do a Time Machine Backup before attempting the updates.