We see that bitcoin's utility as a payment tool has an inverse correlation with bitcoin's market value.
If the market price of BTC goes up, fees for transferring the same value with bitcoin become more expensive.
that is not the whole story. in fact you have forgotten one thing because you are looking at the very recent history. in fact with price rise, fees have gone down in bitcoin terms. for example when price was less than $1 the fees were around 0.1
BTC and as the price went up, the fees went down too. or a couple of years ago fees were fixed at 10k satoshi per transaction.
Indeed I used recent sat/byte fees and prices but this is just for the sake of forming an example.
If you are to introduce more variables in the equation, then you have to be able to prove a correlation. Fee value vs BTC price has a direct connection based on bitcoin's technology alone.
To support the claim that through time fees go down as prices rise, you'd need to look through years of data, see what parts of data are comparable, and account for any connection between the two.
Might be true for some periods, might be the opposite for others. And then transaction volumes must also be accounted for etc. etc. That's much more complicated and doesn't take away anything from the key observation here.
For this example I'll set the sat/byte fee as a constant of 193 sats per byte. Amount of money (in monetary value) intended to reach the recipient can be any constant.
This is a very poor approach at it...
Let's continue your example but increasing the value a bit more:
At a hypothetical price of $9.000 per BTC, the cost of the transaction would be $4.3425.
So for 90k$ per BTC we will have 43$ on average.
And for 900k$ we will have 430$ on average.
By way of example, I'm trying to show that bitcoin's mechanisms makes so there's a direct connection between price and fee-value.
Yes, in a real world scenario there are more variables, but what evidence do we have to support that if prices were to go up that much, the value of fees wouldn't follow suit?
For the record, I wasn't trying to imply that there would be perfect correlation. But rather to show what bitcoin's fundamental's can lead to for fees.
You realize that this extrapolation is pretty lame, even if bitcoin would be worth x amount, people are not going to spend thousands in fees if there is nothing to gain from it.
Excluding a massive FOMO with rising prices when everybody is rushing his coins around there is really no incentive to move your coins at such fees.
And that brings up another problem. Even if the price does go way up and the correlation between price/fee value isn't great, but it's still there.
The problem I show in my extrapolation is still very much present.
Regardless of BTC price, higher fees act as a disincentive to make transactions. So any transaction of value around the range of the fee becomes prohibitive (i.e. if you have to pay 5$ to transact, you won't want to transact anything near 5$).
Arguably, that lowers bitcoin's utility as a payment tool, which is the problem I'm focusing on here.