The chief problem with Path of Exile's idiotic currency system is, as @jozef pointed out, that currency items take up inventory space and are subject to stack limitations, which is a nightmare both for regular gameplay and for managing inventory or bank storage. Path of Exile is effectively unplayable unless you shell out the cash for the Currency Tab, thus effectively turning it into a bank system, so why don't you just use a regular bank that has worked for every other MMO in history?
The other problem is that currency items are just a superficial cop-out. It doesn't matter whether the money is floating gold/silver/copper currency or are actual coins sitting in your inventory, the effect and dynamics are just exactly the same - there is always a standard denominator that all other currency converts to. In Path of Exile's case these are Chaos Orbs.
It's essentially an imaginary "innovation" whose only changes to gameplay are bad ones.
As for the economic and politics of governmental fiat currency, they were invented specifically because the barter system was not sustainable. Older coins had worth directly proportionate to their content (e.g. how much gold was in them), which was not consistent or predictable as we can see from the extremely unstable gold and silver markets today. They were also subject to political whining and willful sabotage - in the historic US, rich bankers preferred a gold standard while poorer farmers preferred a silver standard and this was the foremost political topic for many years.
The solution was to use neither, and instead establish a credit system founded on cheap materials - whose material worth was always far less than a bill's or coin's face value - as a symbol of credit or debt. This is similar to how your balance in a bank account is not real money that really exists, it is a representation of how much the bank owes you. Depositing into an account is literally lending money to a bank, and similarly, holding dollar bills in your hand is holding a sort of public debt that you can trade with others.
Fiat currency is, consequently, largely unaffected by the scarcity or demand for its production materials; its inflation is affected by the raw amount of bills or coins in circulation and how much the rest of the world cares about the country that mints it. This is why so many currencies are worth substantially less than the US dollar, but particular currencies from other "iconic" nations like the UK are worth more.
