I would change the perspective completely. It's not about who will steal Satoshi's coins. It's about wether the bitcoin holders want to sponsor the race towards quantum computing or not. "Satoshi's coins" are either still owned by somebody or they are lost. Owned coins can prepare a migration - even without publicly revealing they prepared - and lost coins are never stolen.

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That's an interesting perspective on the quantum challenge you present. The network's security, and thus all coins, relies on robust cryptographic primitives and a communal endeavour to maintain them.
Sadly you missed a huge group of coins - forgotten wallets and non-bitcoiners. People often forget they had Bitcoin or just don’t care enough to check in on it for *years*. The only way to ensure they get their money is to disable insecure spend paths but allow them to claim via a seedphrase ZK proof. The side effect of this is that you also burn coins not held in a seedphrase-derived wallet (very old coins and a select tiny minority of wallet software).
Why would you assume I forgot about those? The transition has to take years and you can have different strategies for different coins. Satoshi's coins for example could be saved in a non-revealing way by embedding commitments to transactions spending from those UTXOs in the blockchain.