Setting both at same rate would mean bitcoin had no advantage compared to FIAT b/c both behave similar.
We know that isn't the case.
The difference of both is what actually matters.
I estimate the difference to be higher than productivity growth as long as adoption (hyperbitcoinization) is completed.
After that the difference would be at the overal productivity growth / rate of technological deflation.
Don't know if FIAT still existed then or would be fixed to BTC... But doesn't matter here.
Seems quite clear to me.