From a pure theoretical perspective it is inappropriate for a monetary system to put a hard cap on the money inflation process because any such system has to incorporate/support user interactions that have nonzero error rate including fatal errors that lead to the loss of money, a continuous leak of the money to non-existence and reduction of the total supply, hence a currency with capped supply vanishes in some future, and a long time before it happens, it will become obsolete/antique because of its limited supply volume.
There is a continuous leak, but it will not necessarily cause the currency to vanish or lead to a "limited supply volume" (if I am interpreting those words correctly).
Suppose 20 million of the 21 million bitcoins are lost forever. That still leaves 100,000,000,000,000 satoshis, each of which could be potentially be subdivided further into 2
64 "nakamotos", giving a total supply of about 2x10
33 nakamotos. We should be ok for a few more millennia with that.
You get it wrong just like @tromp, and Satoshi I suppose:
Inflation is a mechanism for "distributing" money to fresh actors but the mechanism that you propose, does not help with distribution. To understand the problem deeply, one needs to think in the edges and twilight when your hypothetical precision game is not kicked off and people are dealing with a monetary system's token that is not capable to be stored and exchanged smoothly because it is too rare/expensive and does not cover everyday business.
You suggest that in such a case some guy named Luke jr VI or Gregory Maxwell III shows up and proposes a soft fork for including new transaction formats and more precision points and everything becomes under control again, but it is not the case. Instead, by incremental reduction in availability of money, the economy gradually shifts to other devices, and it pushes the money to an even more antique status, demand decreases while the value preserves or even increases, and it makes everything worse in a positive feedback mechanism.
It is how things work in the real world and if we are arguing in a pure paradigm, there also my argument stands still that such a hard-capped supply ends to extinction. I mean, look at it again, it is so obvious that a system without input dies eventually. Right?
P.S.
I understand that such an antique situation for bitcoin is considered as a good status by some people, Actually we are hearing it over and over about bitcoin being rare and worthy because of this rareness. This is not a technical debate anymore when it comes to such wrong interpretations of bitcoin and I have zero interest to argue with people who believe in bitcoin as an antique article.