Yes, even if the private key is lost. It should be untouched. This is like asking Apple to put a backdoor into iOS “just for the good guys.”
It doesn't matter what 'should' be done. There is money up for grabs, it's nuts to think people will just leave it there. Given that people WILL try to claim it, how should that go?
I never suggested otherwise. This is the part where you now try to continue justifying theft of funds "because someone will eventually steal it anyway." 🙄
It's not theft if you allow the owners to come forward and claim them. In fact, the miners are the best people to run such a system. They have the integrity of the currency in mind.