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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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.