HUDs don't seem like they really impact auto-land. They do impact conditions in which take off is authorised because they can add a synthetic centre line so that pilots are comfortable taking off in low visibility.
For landing existing CAT III landing will complete the entire landing and rollout. Failures (e.g. loss of a flight computer or sensor problems) that would lock out CAT III autoland would likewise rule out attempts in a HUD.
The reason you don't see much real CAT IIIc bad weather landing isn't that it can't work or HUDs would be better, the problem is that sure, now you're safely on the ground but with zero visibility you're stuck on a runway, you can't very well taxi a jetliner when you can't see the concrete you're on let alone the signs and lights. Even a follow-me car won't help, you can't see it.
Garmin's emergency autoland for GA pilots has the same problem, but since it's an emergency feature "Oh dear we took an entire airport out of service for an hour" is an acceptable consequence. The alternative may well have been fatal in that case.
Anyway, people have added e.g. enhanced visibility and highway edge marker HUDs to high end vehicles before. But, that's going to be something you need to train with in order to use it effectively. An airline would send crew on the recommended two week course before they're allowed to fly the modified plane, but we know even private pilots routinely avoid recommended manufacturer training, and cars would definitely be worse. My guess: Tesla would sell a thousand cars with a HUD, fifty drivers would take the free training, ten of them would come away having learnt anything. All one thousand owners would be confident they can now drive at 60mph in dense fog even though the training said "You definitely must not drive at 60mph in dense fog".