The purpose of a PP is not to increase its value over the rate of inflation. Rather it is a way to maintain purchasing power.
When the treasury vault is empty the Sovereign/Treasury/State will tend to 'confiscate' and will legislate and/or tax accordingly.
There are instances in history where holding stocks, gold, treasury bills and treasury bonds each and collectively have lost heavily in real (cost of living) adjusted terms. Of the order of >50% amounts (more than half of wealth lost) for PP like asset allocations.
With the PP you'll pay insurance costs in the form of lost opportunity costs (lower rewards than might have been provided elsewhere for apparent greater security), only to potentially see that insurance/security invalidated when needed the most. By design (Sovereign. State, Treasury specifically targeting 'confiscations'), not by coincidence.
An irony is that stocks - which are often seen as the more riskier asset, tend to be less risky over the longer term than government bonds - which are often seen as the least risky asset. If stocks achieve a 100% real gain over a period of time and then abruptly lose half you've still the same as the original amount. If bonds pace inflation over a period of time but then lose half, you're down by a half. The PP is more inclined to fall into that latter category.
