In my view:
1 Bitcoin will always equal 1/21,000,000 of the total network.
1 Sat will always be the smallest unit of measure on the Bitcoin network.
However 1 Bitcoin will not always equal 100,000,000 SATs. As value per Bitcoin intensifies, 1 Bitcoin will be subdivided further and the new smaller units will then be considered SATs.
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FWIW, I believe the lightning network is already setting the standard 'millisat' (1/1000th sat) for when the need arises for smaller units. As the OP points out, changing a unit of account (even sats) would likely cause way more problems than it would purportedly solve.
If 1 Sat every equals $1, or $10, or even more, then it'll be so obviously needed that the network will be updated. IMO this is just a matter of time.