In the case of fiat money, I think it is questionable if Bitcoin can replace it. Fiat's "innovation" was to adapt money supply to real economic growth without the "limits" of an asset like gold. I can perfectly imagine a "Bitcoin standard" society, but in this case I think there would be replacements to fiat -- and if we think of a crypto-only economy, this would be a strong altcoin sector with continuously growing total money supply.
There are some common similarities that we may be able to apply and compare fiat to Bitcoin existence, but we should know that they entire pattern of introducing Bitcoin does not aligned with what we already have with fiat, but if it happens as intended, it's either we have both to exist and each individual will have to decide on which one they wanted and how they are going to make it more applicable on their demands.
Talking about the value of bitcoin, the incessant printing of fiat currency and inflation altogether, we should be able to arrived at a conclusion which permits that the more we continue with the way of using fiat, there's obvious reasons not to have a change from what has always been, but bitcoin serving an alternative will make everything balanced on an equal rights and access towards a decentralized network, whereby the Bitcoin value continue to increase over time instead of continuing mining without limit, everyone will eventually have Bitcoin even after the 21 million has been completely mined, because it will always increases in value instead of continuous mining as they do with fiat.