I do broadly agree, the "27 years" figure is a rhetorical number that doesn't mean anything in itself. That said...
> If the goal of the question is to work out how long a fiat currency not backed by gold will last before it's hyperinflated into nothingness
That isn't completely fair. The ducat lasted ~730 years and preserved a reasonably consistent amount of value all through that time. Someone holding a dollar in 1971 has effectively lost 95% the value that they expected it to have vs gold. Even as demand for gold has presumably plummeted now that it is no longer officially involved int he monetary system.
Just because they are destroying the value of the currency on purpose doesn't change the fact that the value will be destroyed. It doesn't need to be an unexpected event like a hyperinflation - normal inflation is also enough.
> The ducat lasted ~730 years and preserved a reasonably consistent amount of value all through that time.
Not really. Inflation long predates modern times, there's a reason that the terminology is called "debasement" (adding base metal to gold coins). I don't have hard numbers on the value of the ducat (because that pretty much requires trawling historian journals I don't have access to), but judging from other coins that pop up, the annual inflation rate would have averaged perhaps 0.5% for the Medieval and Early Modern.
Why should a steady 2-5% inflation rate in modern times be considered destructive to value, but not the steady 0.2-1% of earlier periods?
> Why should a steady 2-5% inflation rate in modern times be considered destructive to value, but not the steady 0.2-1% of earlier periods?
Because they are different by an order of magnitude. Over a 70 year lifetime, at 0.2% inflation a coin is worth 90% of its value at the start of the life. At 2%, it is worth a hair less than 25% (at 5%, it would be effectively worthless because the coin has lost 97% of its initial value). That is quite a different outcome - one of those rates I could save using coins and not do too terribly in real terms.
> If the goal of the question is to work out how long a fiat currency not backed by gold will last before it's hyperinflated into nothingness
That isn't completely fair. The ducat lasted ~730 years and preserved a reasonably consistent amount of value all through that time. Someone holding a dollar in 1971 has effectively lost 95% the value that they expected it to have vs gold. Even as demand for gold has presumably plummeted now that it is no longer officially involved int he monetary system.
Just because they are destroying the value of the currency on purpose doesn't change the fact that the value will be destroyed. It doesn't need to be an unexpected event like a hyperinflation - normal inflation is also enough.