Did it ever fluctuate like that when it was pegged?
But you can see that inflation (and worse deflation) had volatility when the us was on the gold standard: https://www.investopedia.com/inflation-rate-by-year-7253832
If you dig into the 1800s the volatility was even worse.
So you have to compare them to other things, which is what inflation (or deflation) measures. And gold pegged usd has volatility to other items in the economy greater than modern fiat usd.
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Edit:
You're near-certainly right that pegging in dollars would means some rate, let's for simplicity presume a constant ratio, between dollars and what it's begged to.
I think crux is what happens if we model two different currencies, one of which is begged, and the price of te commodity in each.
If after the conversion rate you can get cheap gold, that keeps golds value low and pegged currency's value high, I would guess.
Again I think restricting impots in the commodity is necessary to maintain supply.