You can decouple the encryption and decryption keys such that the private key would never be present in any Tesla system at any point in time[1]. And you can introduce a ratchet such that compromising the Tesla car at time t0 would not enable the attacker to decrypt any encrypted data at t[n < 0].
Updating a car with a new key would fix both problems. Old recordings would be lost, of course, but customers hearing "I can't unlock that without your old key" may be necessary to re-establish trust.
Absolutely and that is why you can't use an HSM. Thankfully generating keys on device and storing them on the cloud account encrypted by a passcode works. As the keys are a predictable size you can encrypt them multiple times with different passcodes.