I don’t think it’s worthwhile to pretend that BTC has a stable value.
The way I think about it is - fiat currencies like the dollar have optimized fulfilling as much of the total accessible market, as possible, making sacrifices on the soundness and hardness of the money.
Bitcoin on the other hand does the opposite (and it’s obviously much newer), where it maintains its hardness/soundness at the cost of a slower adoption (relative to fiat).
The instability of bitcoin come from the fact is that it’s significantly lower on the adoption curve, but it maintains excellent fundamentals. Fiat again, the opposite.
I guess the point I’m making is that it’s impossible to measure “stability” given both variables have different unstable properties. Let’s just be honest about it.