Fiat is designed to lose value, 2 percent in some countries, 2 1/2 in others. Bitcoin not.
Bitcoin too, until the year 2150 or something ! Although you are right that bitcoin has monetary mass inflation until then, while many central banks have price inflation targets. The difference between both is (at constant velocity) given by economic growth.
The store of value aspect and the transaction medium aspect of money hangs together, you can not have only the one or only the other. So when you hold, you need to be sure that you can transact. But the volume of transactions that occurs is irrelevant.
I think we're in a chicken and egg problem. Of course, volume can be small, and value (per coin) large, if velocity is small (if most coins are held a very very long time). In that case, you are right, volume doesn't matter much, my formula doesn't matter much, and we are more in a "store of value" problem, and the market share of the aggregate demand for store of value.
On the other hand, if bitcoin is mainly a means of payment, then the demand will essentially be to have "bitcoins to pay with", and the inherent time they are held between obtaining them and spending them, is then more described by my formula. We are then in a market that is essentially driven as "monetary asset" (to buy stuff with).
In reality both will play. But my personal opinion is that the latter will be more important in the medium term (the coming decade say) than the pure store of value. As someone else said, that's not a problem because for the moment, speculation "to the moon" is the driver. But that driver will not - in my opinion - hold on for 10 more years without any fundamental driving it, and only a (pipe?) dream in the far future going for it. This is why commercial adoption is so important, and it has to become a significant part of the demand if bitcoin is to go somewhere (to the moon).
Holding today means speculation that a large number of people will discover the same thing. I think they will, and one of the reasons it goes slowly is the vast amount of nonunderstanding of the value of money problem among people who have understanding money as their job.
That's true :-) However, it may become a self-fulfilling prophecy too. If people commanding large amounts of value are "too stupid to adopt bitcoin", well.... then bitcoin will not be adopted. This is why I think the road of commercial adoption is much much more important than long-range speculation of "the moon". Commercial adoption will rise the demand for bitcoin as a payment asset, and not as a store for value (any longer than the time to spend it). If *that* can support a higher market cap, it may be the main price drive in the coming decade, over promises of "the moon", which will stay hypothetical, in my opinion, for at least many decades (at least the time it takes for the current generation of financials to take their retirement).
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