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 I don't understand.  You have to part with increasingly more valuable satoshis to pay increasingly higher fees. In USD terms, the fees will increase at least as fast as the value of the original $200. 
 Even if we assumed your assumption was correct:

Let's assume an average $12 fee now (probably will drop back to lower levels)

$200 - $12 = $188

If we assume your thesis that fees will increase at the same pace as the savings:

$20,000 - $1200 = $18,800

Yeah, I'd rather have $18,800 stored safely on the base layer, vs storing that amount on L2. 
 Now less than a week later the average fee is around $4 - $5 per tx.

In the above example with a 100x increase in both exchange rate and transactions:

$20,000 - $450 = 19,550. 
 Math 4 the win 🏆 
 Just had a look at the mempool today and the average tx fee is $1.61. 
 i could be wrong, but i highly doubt the fees will increase as much as the value of bitcoin. the fees are based on the amount of data being sent in the tx and not on the amount of sats being sent.