I put emphasis on the word "naturally" because you cannot force a monetary process to establish itself in a few short years. The price and users must gradually reach an inflection point on their own.
It is similar to implementing the Euro as the official European currency. By no means were the governments rushed to scrap their central bank currencies, they were give ample time (about a decade or two IIRC) to phase it in, in stages.
So Bitcoin, and anything that wants to follow it in market capitalization, must be introduced to the public in phases, which could take a very long time.
The rest of the altcoins that do not stabilize can disappear (e.g. Solana), I have no pity for them as they only serve to give larger cryptocurrencies (and crypto in general) a bad name in the news.
The only way volatility would "disappear" is if people began using Bitcoin regardless of its value in Fiat terms. That would mean ditching the "Fiat Standard" in favor of the "Bitcoin Standard". But this is very unlikely to happen since governments and central banks still have the leading edge over the global economy. As long as Fiat exists, Bitcoin won't be able to fulfill its purpose as a currency for cross-border payments. It's only useful as a store of value.
If you really want stability, then stablecoins or cash are your only options. I hope someday Bitcoin becomes the global unit of account in order to truly decentralize the world. Just my thoughts