It seems to me that Bitcoin volatility is a direct consequence of the fact that not all 8 billion people on planet Earth have realized its value and significance. When all 8 billion people realize the significance and value of the first cryptocurrency, then its price, in my opinion, will stabilize.
I agree that "number matter", and of course if everybody already owned Bitcoin its price would be stable.
But I think Bitcoin can already be less volatile and much "safer" to invest with a much lower number of users. In reality, I think if all the 300 million users we have now according to estimations like Triple A's, used Bitcoin exclusively to save money for longer periods (DCA & HODL) and not to trade, then we'd already made a big leap forward. Basically the idea is to move on to a real store of value, like the (already mentioned) "Bullish Case for Bitcoin" envisioned,
I don't think everybody has to use Bitcoin. It would also currently not be possible due to the scalability limits, even if they used Lightning and Bitcoin on other blockchains. If you mean with "recognizing its value" that most people at least don't oppose Bitcoin (and call for bans or harsh regulation), then I fully agree. Also here a stable majority would already be enough, there will always be some naysayers.
Nation-state reserves are probably not that essential for lowering volatility. We could even see an increase of price swings, if the speculative users and Bitcoin influencers use every new "reserve announcement" to generate FOMO and then take profits a couple of weeks later tanking Bitcoin's price 20-30%, like we saw in the last months. On the other hand, governments with Bitcoin reserves would of course not likely ban Bitcoin, that would be a point in favour of reserves.
It is quite possible that in the future, digital fiat money of states, shares and bonds of corporations, tokens giving the right to own a share in all world assets will be issued on the basis of Bitcoin.
I think Bitcoin could indeed work as a "value anchor" for other assets -- including some fiat-like currency concepts -- once it stabilizes. But the Bitcoin blockchain doesn't need to be overcharged. Even Lightning would probably not the ideal solution for shares and bonds. As these assets are centralized due to its very nature, I don't expect many changes to the current way we trade these assets on centralized exchanges operated by financial giants.
But once Bitcoin was used as a value anchor, i.e. exchanges would add trading pairs with BTC, this probably help a lot too to establish Bitcoin as a "safe haven" asset. The more it is traded against assets of differend kinds, the more liquidity we'll experience, and liquidity also leads to stability and "safety".