Well, it depends on how high is the fee. $1 for the transaction is nothing. And even $10 is not much if you're transferring thousands of USD in Bitcoin.
Take note that tx fees should be valued in sats/vbyte and not in dollars or any other currency. We used to make tx's with as low as 1 sat/vbyte before, right now fees are not as bad as it was during the ordinals craze, but not as low as it was when tx fees were very cheap. It is worth mentioning that people make a lot of micro payments using BTC, and if what they have to pay in fees is equivalent to $1 or above, then it may be considered expensive. However, like you said, if you are sending a large amount or making cross-border payments, then that amount in fees is good.
Yes the problem here is we are happy when the value of Bitcoin increases and we should be aware that the fee is calculated in SAT as you have clarified and it's not the increase in fee structure but rather the value of SAT gets increased, since this is not based on USD we feel pinch in our pocket when making transactions. This is something which we cannot resolve and the two options left to use would be either don't make micro payments through BTC when you feel the price is high as we compare it with our currency, second use any other altcoin for micro payments as I use TRX for such purpose and we need to understand that fee will increase when the value has increased and we cannot compare it with USD or other currency but SAT.