Any securities, commodities and assets can be a trading pair, so volatility will always exist even if fiat is gone completely.
Bitcoin supply side volatility is built in with the hard cap and halvening.
But it's not impossible to it becoming more stablised if the properties become more appreciated and accepted as gold.
The bigger risk imo, is early nations that adopt Bitcoin enmass, is most vulnerable to speculative attack. Before you say but it's no good for any one, this has already happened in 1997 Asia financial crisis.
I agree completely, the thing is that bitcoin now is treated as an asset, but adoption implies that it starts being treated as what it's intended for: being a currency. No base currency is volatile against itself, for 1 USD = 1 USD, but only prices measured in that unit are considered to be volatile (even if it's the fault of the mismanagement of the currency itself). The same is pretended for bitcoin when we refer to "mass adoption". There is nothing like a "mass adoption of a specific asset", for we can't pretend that every person in the economic web haves to buy a house to use it as currency for every exchange. Gold became an "asset" when the gold standard was abandoned, prior to that gold was the currency in itself, and currency units were determined as fractions of gold units. Nixon did so much damage...