Actually, a fiat currency IS a type of planned economy. With a fiat currency the government can manipulate the value of its currency. In many, many cases said government finally gets too greedy and manipulates the currency to the point that no one trusts it and the value plummets towards zero. In any case, though, controlling the nominal value of the currency is a tool governments with fiat currencies use to manipulate (i.e.: plan) their economy.
I think fiat currencies are inherently risky due to the high probability of government overreach, but I disagree with your comment that all fiat currencies are doomed to fail. The only failed fiat currencies that can be mentioned in history books are those that have failed. Ones that haven't failed still exist, so their failure is not recorded. You therefore cannot invoke history to claim that all fiat currencies fail as long as there are fiat currencies still in existence that have been viable for long time periods. (This is not to say they won't fail, only the the "history shows" argument is fallacious).
Finally, saying that "all systems of humanity eventually fail" suffers from the same sort of problems. I can point to many human systems that have existed for millennia and continue to work for us (think agriculture, trade, language, writing... none have passed away and few seem destined to do so in the foreseeable future).