So tell us your non-arbitrary and useful measuring point that provides for a safe gap that fits between car length (like car length is a non-arbitrary useful measurement) silly and that-guy-is-so-close-that-if-he-sneezes-he's-going-to-be-sitting-in-my-back-seat.
I'll stick with the where the tires meet the road thing as it is easy to do every time with any vehicle.
Define "safe". If personal safety is your goal, then it's largely moot with modern cars. To get hit hard enough to metaphorically be in the back seat with a direct rear impact in a modern car pushing you into another car, the collision would have to be at such an excessive speed that no reasonable safety gap (IE any of the distances being discussed in this thread) would account for it.
I generally aim for 6-8 feet. That's plenty of room to get around somebody (although that's not generally possibly due to cars in the other lanes in most major cities), plenty to avoid normal rollback from somebody with a manual, and plenty to avoid hitting the car in front of you in an average fender bender which is the criteria most people are providing here. Before you ask, yes, I've been rear-ended while stopped at a light before.
If you're trying to allow enough space that you won't touch the car in front of you in any "reasonable" situation, then you're drastically underestimating the amount of room you'd need. Your average sedan is about 17 feet long. A rear end impact at 40mph from a moderately heavy (IE any of the millions of medium trucks/SUV's on the roads) vehicle is going to push you a solid 35+ feet. There's a variety of calculations on this from people way smarter than me on a various physics forums as well as observations from videos and in person experiences. If you want to plan for worst case....
https://youtu.be/gJIgD1wQaAU?t=44
There's other more "normal" examples in the same video
https://youtu.be/gJIgD1wQaAU?t=111
Impacting car is a pretty light car (Mitsubishi Lancer, roughly 3,100lbs) and started braking prior to impact. Impacted car still rolled well over it's own length in distance.