"Don't send to 1BitcoinEaterAddressDontSendf59kuE. These coins are lost."
One day computers will be able to hash the privatekey for this address or for addresses with no access to it. Therefore coins should be removed after mining from the coinbase address to show that someone has access to it. Otherwise they are shalecoins waiting to be "remined" or "fracked" one day.
That's not how it works, you generate public key (using ECDSA.secp256k1) from private key then perform RIPEMD-160 and SHA-256
Also, the only way to prove some has access to that address are by sign message or spend coins from that address.
Even Quantum Computer won't able to obtain private key of that address because it's public key isn't known.