As goldpelican says, its more of a privacy issue than a tax issue.
Once you hand over your ID, you've got no idea what happens to it. It should end up sitting in a secure filing system at the dealers, but it might end up somewhere else being used for nefarious purposes such as setting up a bank account or credit card in your name. A detailed profile of your purchasing habits also has the potential to be seriously misused.
To illustrate, there was a security company in Sydney a whale back that was scanning the IDs of people entering certain "problem" nightclubs in case they were later found to be causing trouble in the venues. It turned out that the security company was just dumping them on a portable, unencrypted hard drive at the door and later sending them, unencrypted, to head office were they were merged in with IDs from all the other venues and stored, again unencrypted, on a web server with the password stored in plain text in another file that anyone could see by looking at the website's directory structure. That means a full copy of your name, address, date of birth and photo ID was out there waiting to be stolen and all for the privilege of being able to drink expensive booze in a violent nightclub.
The ATO at least have to follow procedure if they want to go after you. For everyone else out there, you're fair game. Be worried about everyone else.
