Exactly. As long as Bitcoin is measured against Fiat, it'll never be able to achieve independency from the existent monetary system.
To overcome this phenomenon, Bitcoin would need to become
the global unit of account, much like the dollar is today. This goes beyond just the abandonment of fiat currencies.
Imagine if fiat currencies are abandoned and people return to using gold and gold-backed notes as their primary unit of account. In that situation, I think bitcoins would at best occupy the same space that gold already occupies in relation to fiat today.
Bitcoins would be treated like any other commodity: When economic turmoil strikes, speculators would sell them for safe haven assets like gold, gold-backed notes, and government bonds whose credit rating would be linked to gold reserves.
Besides that fiat money religion is everywhere, I also don't think it is a good idea to make bitcoin a standard unit of account, since the production cost (mining cost) rises too fast. The cost basically decided the value of a coin, and if a coin's value rises very fast, and you use it as unit of account, everything's price (counted by bitcoin) will drop so dramatically that merchants simply have no way to make a profit
The unit of account should be stable, and can not be created out of thin air (against debt). So I promote to use energy unit like Jole or KWH as unit of account. Since everything's production eventually goes back to the use of energy, it can be a very stable and object measure of value
By using energy as unit of account, there will be different view of value. For example, currently when a barrel of oil price crashed from $40 to $20, and people use USD to measure value, they will call oil price crashed. But if you use energy as the unit of account, a barrel of oil always contains same amount of energy, so it is just the USD suddenly get more valuable