Many people have speculated that the fees will just keep going up linearly
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Linearly? They go up exponentially! There are always more low-value transactoins than high value transactions (think Zipf law). Which means if growth is linear (which is not the case), even then fees would go up exponentially.

Because transactions pay whatever they must to stay on. So fees are determined at the cut-off point by the last person to give up on Bitcoin completely (or for that use-case).

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