As the primary author on that paper, allow me to make some nitpicks. The paper presents a scheme for merged consensus, not merged mining/staking. Unlike merged mining, merged consensus is a consensus protocol that can be introspected entirely on-chain (with some optimism and synchrony assumptions). This allows for permissionless trust-minimized side chains.
This intuition can be found in my post on Minimal Viable Merged Consensus, namely
It’s important that the side chain’s consensus protocol’s safety be guaranteed modulo trivial assumptions, otherwise you’d be scaling throughput at the cost of funds being easily stolen. You can’t get this guarantee with merged mining/staking, so that avenue of scaling is largely a dead end. (Merged mining only provides security against external attackers, not state safety.)