It has nothing to do with "acceptance". Volatility will go down (not be totally eliminated however) with wider spread adoption.
It has everything to do with
acceptance rather than
adoption. Gold is not adopted by most (most people do not own it) but it is accepted by most as having value. It is the acceptance that is the important thing, not how widely adopted it is.
You seem to agree that gold is a store of value and yet the spot price of gold isn't stable. Just look at a chart. It may be less volatile than Bitcoin but it's not stable.
I know. I never said it was. I merely said that the
ideal of a store of value is that it has a stable purchasing power. (Well, ideally it would always increase in purchasing value, and never devalue even in the short term). But gold is seen/accepted (there's that word again) as a store of value, even if the vast majority don't adopt it. How good or bad in the short and long-term is up for debate, of course.
If you define stability as in pegged to the dollar, there are stable coins for that. That's not a store of value though since the dollar's purchasing power only goes down.
I don't define stability as that. I even explicitly stated "it would hit a stable range whereby 1 Bitcoin could always buy the same value of products". No mention of the dollar. Just of purchasing value.
If you pick a Jan 1 at anytime in the past, Bitcoin will buy at least as much now as it did then. That makes it a store of value. In addition, it is also a good investment since it has gone up, as an asset class, more than any other asset class. Gold is not a particularly good investment, it's just a decent store of value.
That's true of any number of stocks, such as Amazon, Apple etc. That just makes it an asset worthy of investment consideration, not necessarily a store of value. And until it is more widely
accepted Bitcoin has the potential to plummet in value. When that risk is removed through wider
acceptance (i.e. whether actually used or not) that it has value, it will remain as a speculative investment asset. A good one at the moment, for sure. But I'm certainly not invested in it as a store of value, but rather purely as a high risk/reward asset. Which is what most people are invested in it for.
What more could someone expect from Bitcoin as a store of value?

It's not a great currency, we have the dollar for that in the U.S. In more inflationary countries Bitcoin could be used with a secondary layer (Lightning Network) on top of that or one could use Ether or Ada or whatever.
It needs confidence and acceptance by the wider community as having value, even if they themselves do not adopt it. Gold has that in abundance.
I don't see how Bitcoin is anything though if not a better version of gold.
It has the potential to be, for sure. But Bitcoin only has value at the moment to those limited few that perceive it to have value... which is a tiny proportion of the world. Compare that to gold which is almost universally accepted as having value. That's what Bitcoin is currently lacking. And while countries such as China do their utmost to keep that acceptance down, it's got a long road to gaining that wider acceptance. The wider it goes, the more a store of value it will become, even if adoption remains at today's limited levels.