The blockchain itself is for most cryptocurrencies already quantum-proof, since they rely on hashing blocks until some number of leading zeroes is met. That is the blockchain part.

What the paper seems to target is quantum-proof account management, a problem which atleast on the Ethereum blockchain is trivial to solve at the moment with some inconvenience and with later Hardforks implementing the account abstraction, will be part of how the chain works. Everyone can then just use a Lamport/Merkle signature, SIDH, New Hope, whatever, as long as it can be implemented on the EVM.

I'm not certain why we need to throw quantum-computing at the blockchain until some arbitrary amount sticks that can be declared "secure".