Yes all monetary value is ephemeral, intangible and based on the belief and good will of the marketThat's an overly simplistic view of the value of money. If the value of money were only based on belief, then one would except sudden collapses of monetary value without any connection to the real economy quite regularly. In a sense, money would be like the cartoon character who defies gravity until he looks down.
In reality, the value of money is based on people's demand for money. This demand is largely circular (the store wants money in exchange for goods because that's what the suppliers demand, and the suppliers demand money because that's what their employees demand, who demand it because that's what the stores want, and so on).
However, there are two decidedly non-circular sources of the demand for money. One of these sources is taxation: If the government decides that you have to pay your taxes in currency X, then there will always be demand for that currency. Even if your employer pays you in Bitcoin, you will still have to pay your income tax in whatever the local fiat currency happens to be.
The other source is debt payment: If you are in debt, you have to make certain payments (under threat of losing your house etc.).
These two belief-free sources of demand for fiat currency are the "base case of induction" for why fiat currency has value. They ensure that the viability of fiat currency does not depend on belief.