Will Bitcoin always be volatile?

I've been hearing that as the market cap increases, the volatility will decrease. It's probably already happening.

But the other day I was watching one of Peter McCormack's videos where he was interviewing a VC and the VC said Bitcoin will always be volatile, because it has a fixed supply. He called it a rigid monetary policy, and said fiat is stable because the central bank controls the supply. I understand that when the price rises, the central bank can print more money to bring the price down; and when the price goes down, it somehow 'sequesters' it to bring it up? (although I'm not sure what such sequestration would look like? does it have anything to do with bonds?). So he essentially says interventionism is needed to keep the price stable; an idea I don't particularly like.

Another thing with Bitcoin is that a lot of it is in the hands of a small number of whales, who can manipulate the price. With fiat that's not the case, because no one wants to hold massive amounts of a deflationary currency with an unlimited supply. Since there is no such thing as voluntary fiat whales, the central bank / government can be that whale and have a monopoly on manipulation, for better or worse.

But I also suspect the relative stability of fiat is due to the fact we denominate the prices of goods and services in it. The value of a fiat currency can also swing a lot, e.g. when the BoE kept the interest rate unchanged in the November meeting, against expectations, GBP dropped against the other major currencies. But the prices of groceries etc. didn't change overnight. Prices lag behind for many reasons: it's not practical (and costly) for merchants to update them every day, they don't want to put their customers off, goods in retail were often bought in wholesale months earlier and can still be sold at a profit while stock lasts, some of the goods are domestic and some are imported, price control (e.g. rent control, energy prices caps). Also, employers generally only review their employees' salaries annually, only ever increase them and do so carefully, so they don't feel pressured by the market to decrease them when the currency strengthens, for which there would be no acceptance. Employees want predictability and don't want their wages to go up 5% one month and down 5% the next - so we give them seemingly constant wages, kind of sweeping the real volatility under the carpet and smoothing it out.

Bitcoin, on the other hand, is not used to denominate the prices of goods and services in; it's pretty much only traded on exchanges, so the prices can go up and down all they want and the people that feel the volatility's impact are generally not the kind of people that mind it.

If/when the world switches to the Bitcoin standard and everything is denominated in BTC, I suspect the same price lag effect will give it stability. But then, the world probably won't switch until BTC is already somewhat stable.

What do you think?