Where does the base assumption that it has to take over in a decade come from? If you give it a century then its starting to look much less inflationary than holding USD.
You could play a spreadsheet game of finding a length of time to take over such that its always just a little more stable, just a little stronger, than the USD.
Finally another base assumption is that "being a major player" is the only success condition. Would it be an utter failure if instead of becoming as big as the USA economy it never became larger than the Australian economy? Australia isn't all that awful of a place, you know.
Why would anything on the Internet take a century? If you look at a spreadsheet it actually turns out that there is no length of time it could "take over" such that it is a little more stable, and a little stronger, than the USD.
For this to happen, for the reasons I mentioned it would have to inflate at between 0-10% per year. If we go with the ultimate limit of 21 million bitcoins, this means that the price has to move down over time.
That cap is at $5.6 billion. If we assume no mining and a 6% inflation, that would have to move down $5.6, $5.26, $4.94, $4.65, $4.37, $4.10, $3.86 over seven years (in real terms). That is just a very low market cap for an Internet currency.
And if it's NOT an internet currency?
Then what keeps anyone tied in to bitcoin? Gold at least has the lock-in of millennia of world-wide acceptance, as well as an absolute scarcity in the sense that no other element has quite the same characteristics, including verifiability. Further, Gold has significant costs to move and exchange (including transportation, theft prevention, insurance, further verifiability, and so on.) So even if someone thought Gold was on the decline, it is not nearly so simple to move to something different.
Bitcoin has nothing that makes it unique on the Internet - except adoption. So if it is NOT getting adopted, anyone can move away very easily. If it IS getting adopted, deflation (scarcity of its supply) is a natural check to that, and people will stop adopting it for the purposes listed.
You say I claim "being a major player is the only success condition". Not exactly, though that is the situation I analyzed. Why?
Because on the Internet, you can't normally play second fiddle to someone's leading technology. There is first fiddle (violin) followed by fourth viola.
If people don't find bitcoin the most useful Internet currency, they can liquidate their holdings in it in 10 minutes * the number of confirmations they'd like. That's it. If they want, they can never use bitcoin again and not lose out on anything.
Coupled with the natural mechanism keeping it from reaching large adoption as a leading currency, this is a dangerous formula that results in a shallow market driven by speculation, based on bitcoin's historical performance and its unique properties. As there is no general acceptance of it as a currency, and very good reasons to think that such general acceptance can never materialize, bitcoin simply is in an extremely precarious situation.
(Finally a small quibble. I actually didn't compare with the U.S. economy, whose GDP is $16.8 trillion in a year. In terms of wealth, "The financial position of the United States as of Q4 2012 included ... a total of $91.72 trillion" [1]. That is net worth, obviously some entities will have both debts and assets, all of which is of some value to someone. So I really was talking about a very small portion of the economy, just the active money supply and nothing else. 7 trillion barely is enough to denominate just 5 months of GDP in just the United States alone, and is comparable to the market cap of all gold ever mined - which sees fairly low usage as a currency. If we imagine that the whole worldwide Internet is using some currency, it is quite a reasonable number on its market cap, in my opinion.)
You could play a spreadsheet game of finding a length of time to take over such that its always just a little more stable, just a little stronger, than the USD.
Finally another base assumption is that "being a major player" is the only success condition. Would it be an utter failure if instead of becoming as big as the USA economy it never became larger than the Australian economy? Australia isn't all that awful of a place, you know.