Lets say by 2020 the fee costs $100 for a bitcoin coffee transaction. However lets say fiat inflation rises really high that in 2020 a cup of coffee will cost you $10000 in new york. So wouldn't a $100 bitcoin coffee transaction fee be cheap anyway in 2020?
Also when bitcoin goes to the moon and is worth $million each then wont inflation make that million dollar bitcoin useless as a can of coke might cost 40 million dollars due to hyperinflation.
Can bitcoin truly be independent without any association with fiat money whatsoever?
This is based on the assumption that Bitcoin will suddenly become the biggest currency in existence and take over the world. This is very unlikely.
Wouldn't a $100 bitcoin coffee transaction fee be cheap anyway in 2020?
Let me make it clear.
No one is going to pay that much for a transaction fee, they don't
care how decentralised and independent it is because they'll go back to fiat or to an altcoin.
There's no reason why every fiat currency is just going to hyperinflate and become worthless. It's very unlikely if they're competently managed. Bitcoin's price will only grow much further in this state if it's no longer viewed as a day to day currency but a currency for large transactions and as a store of value.