I propose a redistribution method:
>If an address did not have any activity in let's say the last 100 years the address is considered lost and the bitcoins are free to be mined in the next block.
To prevent losing your bitcoins you make sure to transfer them to a new address every 100 years (I am not aware of any other method of "proving" you still have access to an address).
This is same to not your keys not your coins logic. Lost Bitcoin or not, We shouldn’t decide on other coins fate if we don’t have rivate key. We can consider it as a treasure waiting to be discovered because not all lost coin is due to lost of private keys. Some of them is just owner died without transferring ownership to his/her heir.
Redistribution coins like this will lost the purpose of power holding or something since we are redistributing coins that is not moving without any verification that it’s really lost and unrecoverable. Best scenario here is a family passing Bitcoin from one genration to other generation.