Yeah, the people who complain that it should be stable don't actually know what they're asking for. You want stablecoins, you get Tether that's losing it's value the way fiat is almost, relative to existence. You want something you know is always worth the same in purchasing power? Then definitely you want something like gold.
I agree with your general point, though gold doesn't necessarily hold its purchasing power. Historically, it hasn't beaten inflation. The truth is, there is no such thing as stable store-of-value. The value of gold, like Bitcoin, is speculative and is at the mercy of the markets.
That's why I like to hold gold (and BTC) during bull markets, but during bear markets, my capital is usually parked elsewhere.