What is the estimated USD fee price in BTC when Bitcoin is worth 1 million dollars in the future?
I think no one can read the future but some things can be said with high confidence and I will try to point them out.
First I think it the conversion to USD does at best make sense for cosmetics thus I will do most computations in the more natural form of satoshis and confirm only at the end if necessary.
if the average feerate in a block is x sat/Byte and with 1 MB blocks we will have a total fee of x Million satoshi per block. This is equivalent to x * 0.01 BTC.
Assuming 2500 tx per block we would end up having
x * 4,000 sats per transaction. (I guess with taproot, schnoor and signature aggregation we could stuff in a few more tx.)
as 1 sat / byte is the absolute minimum fee these 4,000 sats would at a 1 million usd / BTC boil down to $40 per transaction which would have to be multiplied by the feerate x which is any number larger or equal to 1.
I see it from the perspective of Lightning Network rather than from the perspective of making on chain payments. It seems like a reasonable fee to open your channels and be able to transact as often and frequently as you wish. As far as I know it is currently not clear how fees on the Lightning Network would evolve.