I don't think this is precise. Inflation of an asset means that the asset itself drops in value, relative to the value of other goods. For example: when prices rise, the USD itself would be inflating because would then take more USD to buy goods.
Bitcoin is rising in price compared to the USD. So it's not "inflating." If we treat Bitcoin as a currency, it's deflating because right now it takes fewer Bitcoin to buy goods than one year ago.
This is also why "asset inflation" is not precise. The asset itself is not inflating, it is actually deflating wrt. to other goods.
That assumes an asset can be used as a medium of exchange. In its current form, BTC is not a medium of exchange, it's a store of value.
In other words - the word inflation has to do with purchasing power. If the asset isn't used as a way to purchase then comparing the characteristic of inflation is basically pointless. It' be like saying "trees are inflating as an asset". No one makes purchases using trees so the concept is irrelevant.
But you're right that Bitcoin is mostly used as a speculative investment, and not to actually exchange goods. (That's not very convincing to crypto-people, though.)
It more accurately conveys the fact that 1) the assets are increasing in value, compared to a basket of goods or the USD; and 2) doesn’t imply that the asset is a currency.
I'm afraid this ship has sailed.
Demand-pull inflation in fact is exactly what is happening with Bitcoin and bitcoiners would agree. There's huge demand for bitcoin and an ever reduction of circulating supply. What that means is that it can maintain/increase purchasing power incredibly relative to other assets that have unconstrained and erratic supply (fiat).
Maybe you are trying to say that the USD is inflating (w/ demand-pull inflation) because USD is becoming less valuable, relative to Bitcoin.
But that theory is still problematic, since you can't measure inflation against just one asset. An asset might appreciate because of a shift in consumer demand -- the currency itself might not have "devalued." Instead, a better way to measure inflation is wrt. a basket of goods, like CPI. CPI has not changed much in the last year, which implies that the USD is not inflating much.
How about another two? Like equities and real estate. Still not inflation?
CPI is a scam - it now includes 80,000+ items muting the shit out of the dramatic price changes in the stuff you actually want and need.
Consumer prices are flat, but the money printer is making investing assets expensive. That's fun for last year's investors but not next year's.
In economic terms, Bitcoin is inflating as an asset. Specifically, it's demand-pull inflation.
Bitcoin isn't even uniquely positioned to protect against inflation, other than the mistaken public belief on that topic. Inflation is an increase in the price of assets, so investors can (and do) escape inflation by investing their money.
Ironically, Bitcoin's limited supply disincentivizes holders from investing their money.