As usual, technology isn't the reason. It's marketing, profit per unit, and profit in maintenance phase.
The first part does minimal initialization and then gives control to the second part, which is where most of the functionality is.
The first part is also the part responsible for implementing the firmware update protocol and the reset procedure. The first part would either not allow any update to replace the first part, or it would only allow the first part to replace with factory signed firmware.
Alternatively (or in addition) they could have a diagnostic connector that lets external hardware read the firmware memory. You could then do the factory reset on your used car, and then hook something up to that diagnostic connector and have it compute a hash of the firmware that you can check to make sure it is the right firmware. An Arduino should be sufficient as the thing to read and hash the firmware.
Then, if you want to be sure that the firmware isn't hacked, simply remove the SD card, put it in a computer, and verify the contents. If paranoid, overwrite the SD card with the official firmware. If extremely paranoid, throw away the SD card, buy a new one, and write the official firmware to it.
E.g., rms says he used a Lemote Yeeloong because of its free BIOS, but AFAIK he couldn't have reprogrammed it unless he removed the BIOS chip from the motherboard.
Similarly, you move into a new apartment and the super gives you the key (to the door, not a cryptographic one). You installed a new lock, right?
Cursory searching reveals the procedure for manually adding blank keyfobs to Audis, but what you describe above seems... a fairly technically complex system to take on faith. (Given the article we're talking about)
Modern keys are complex things. Gone are the days where you can have a piece of metal re-cut for $5 at Home Depot. A replacement key for modern cars is an expensive proposition: they have to be custom-ordered from the factory (with proof of identity and insurance) then programmed by your dealer. Replacement keys for modern Audis/BMWs/Mercedes run $300-400 all-in. (Remember that scene from Gone in 60 Seconds? And that was 15 years ago. And also a movie.)
You can buy blanks, sure, but without programming, it's nothing more than a hunk of metal.
Is it somehow possible to "clone" a key? Never underestimate hackers, but it ain't easy. Per Brian-Puccio's use-case, unless the previous owner is presenting auto exploits at DefCon, you don't have to worry about someone having a copy of a key you don't know about. (And if they've lost it, you can go to the dealer and have it un-registered.)
Aside: Google around for articles on new car theft: you'll find that no thieves are copying keys or hot wiring or anything like that. In fact, the "new thing" is to get a signal amplifier that allows a car's keyless entry/start system to "find" a key that's sitting 100 feet away inside someone's house or office, then just drive away.
Both with pros and cons, ofc.
I see at least two ways to implement that, but I certainly don't see how practical they are, if implemented at scale:
1) Every component has unmodifiable update logic that supports just that: factory reset for itself, and propagating it to the subcomponents.
This is still where we can say "the owner does not own the car", but in this case it could be treated as a part of hardware (that could not be modified either), rather than "user-space" firmware.
2) Allow easy reinstallation of the critical electronics components, which can be bought from the manufacturer. I don't quite like this "hard" way, but it's a possibility.
If the hardware of the firmware is tamper resistant you can pretty much be sure that it's unmodified. If the attacker can modify tamper resistant hardware I don't think that the car is your first concern.
Remote control over your breaks/steering is a pretty scary scenario. Someone having your physical keys mostly means they can steal your car.
1) By default the cat is "locked", and uses a manufacturer-issued public key to verify the signature of updates
2) A car owner can "unlock" the car, by creating a key pair, and asking the manufacturer to add / replace (debatable) the new public key to the car. Right after that, the owner has an ability to modify the firmware, but everything is still secure. And it's up to the adult owners to manage their private keys and be careful with updates.
3) There should be a simple way to factory-reset the car (with either the owner, or the manufacturer signature).