You basically assume that the fiat currency would depreciate due to increases in money velocity, but how can it increase if people won't be spending their bitcoins? In other words, you set up mutually exclusive initial conditions, i.e. explicitly asserting that people will hoard bitcoins and implicitly assuming that they are going to spend them. Then you proceed to draw an impossible conclusion, which is Bitcoin destroying fiat. However, in that case you wouldn't even need Bitcoin as any fiat should quickly deteriorate on its own for just being inflationary. You see, there are huge holes in your reasoning
No, you just didn’t get it right. I did’t not refer to the overall “money velocity.” We have two separate monetary supplies: fiat and BTC, each with its own metrics. Currencies are exchanged at a market rate (there is no legal tender law setting a hard ratio.) Under such conditions, the demand for the fiat currency will tend to the spending side, while the demand for BTC will tend to the saving side. This disproportion will lead to the increase in velocity of fiat’s circulation, which will start a hyperinflation feedback loop ultimately leading to the extermination of the fiat currency
And how's the "demand for Bitcoin to the saving side" is going to hurt fiat?
Moreover, the conclusions you arrive at should hold true even without Bitcoin. According to your assumptions and premises, any fiat currency should quickly collapse just because it is inflationary as inflation causes an increase in money velocity, and the latter should push inflation rates higher. But it doesn't happen in real life unless the government goes nuts with printing money, and then it is just hyperinflation caused by excessive money printing that has little to do with changes in money velocity
Under such conditions, the demand for the fiat currency will tend to the spending side, while the demand for BTC will tend to the saving side
Which is otherwise known as Gresham's Law. People will save Bitcoin and spend fiat, with bad money driving good money out of circulation