If you throw in a century of economic growth then 9 digits could be plausible as well as follows:
Suppose Bitcoin absorbs 10% of M2 and the M2 growth rate of roughly 4% persists for a century.
That would imply 1.04^100 = 50.5x growth over 100 years.
That would bring the 10% estimate from 3m per Bitcoin to 151.5m per Bitcoin 100 years from now.
These kind of valuations are highly flawed. If bitcoin ever absorbed even a fraction of "M2" growth it would be largely as a pure unit of account, not a store of value. In other words you'd (by definition of M2) be talking about BTC denominated bank deposit accounts and money market funds and all kinds of other fractional reserve derivatives.
Use of bitcoin as a unit of account is something hodlers tend to ignore. If bitcoin ever became a currency we would not be exchanging actual bitcoins, but bitcoin denominated credit just as we use arbitrary units of credit today. So you can't just divide random incumbent money supply figures by 21 million to get a price for a future BTC. Since it's limited in supply it's an asset and will always be an asset.
If you denominate, say, UK GDP in bitcoin then it's around 0.3 Trillion BTC. The GDP can be 0.3 Trillion BTC even though there are not that many bitcoins in existence.
Maybe flawed, but only partially. If bonds are issued, then this is not a unit of account, but an actual asset that contributes to the overall size of assets, is it not?
Bond market in US is 82tril, global-above 100 tril.
I can redeem a bond and get currency/cash.
Analogy: water in the lake is still a part of water present on planet earth.
In theory it works like that but in practice it doesn't. Even in the Bretton Woods system there was a "notional" convertibility to gold. But there was still far more currency in circulation than there was gold in existence. The value of gold was simply pegged to a multiple of the dollar ($30 I think).
Lets say you had 1 bitcoin and you issued a bitcoin backed bond. You now have 2 effective bitcoins in circulation - the real one and the bond. The original doesn't cease to exist just because it's backing a bond. Similarly, crypto exchanges inflate the bitcoin money supply. We deposit our bitcoin on exchanges and they create these "synthetic" bitcoins for us to trade. Meanwhile the deposited BTC are still in circulation on the blockchain.
People tend to think that they're "locked away" and out of circulation, but they're not. The new synthetic ones are added to the supply. The exchange can do what they want with the deposits - it just depends on the contractural terms.
So the "21 million" limit is not really a limit. The bitcoin supply can be expanded in an unlimited way and will be simply through its use as a pure unit of account, same as any other asset.