I agree that bitcoin is sort like a form of money but no way it could be the same as fiat currency because people trade their fiat to bitcoin which will then the price of bitcoin decided depending on the demand of the people wanting to have bitcoin.
Again, this is just my opinion because for me it seems that cryptocurrency has been exaggerated, over rated and fiat currency is being overkilled.
That's your perspective and it's ok to think that way but do understand bitcoin isn't fighting for it to be like the fiat system. Bitcoin is totally different from that scam that the government have used to decieve the masses for years. You speak of people using their fiat to trade bitcoin so bitcoin can't be seen as a money from your perspective what about if the statement is turned around in the sense that people used their bitcoin to buy fiat because this also happens.
Currency are meant to be traded, if any currency can't be exchange for another then it means, it's not been valued. The euro is traded with the usd those that make them less of a currency? I doubt so.
You can have bitcoin but if it is not being tradable to fiat currency then your bitcoin has no value at all.
What gives a currency value? The value of any currency can been seen in its demand that's its ability to be exchange for goods and services which bitcoin does perfectly. Bitcoin would still be valued without it been paired the US dollars. There's a demand for bitcoin, which result from its unique features of decentralized, limited supply and digital mode of operations which is something the whole world is buying into.