I don't see why it shouldn't. I will always want the best SoV in exchange for my services, why would I want something else? If I need to exchange the currency for a SoV everytime, I might get the SoV from the get-go.
The characteristics of Bitcoin that make it such a good store of value make it really bad at these. Computation-heavy proof of work creates a secure and immutable network, but also makes it more expensive and slows down transaction times. It's scarcity makes it a speculative asset prone to booms and busts, but gives it the best chance of long term value growth.
But I guess what you're saying is that as a buyer, why would I not want my money to live as a strong store of value up until the point of transaction, which I think I agree with. It'd be nice if you could own Amazon stock and then pay at McDonalds with USD taken out of the value of those stocks (though tracking capital gains would be annoying). In that situation though, Amazon stock is the good store of value and United States Dollar is the good medium of exchange.
That can be done with Bitcoin today. Download a lightning capable wallet in the appstore of your choice and post an invoice, I can instantaneously pay that to your wallet with near zero fees.
> stable value
That is basically what I was saying earlier, we don't know the correct price yet. However bitcoin is only volatile upwards (if your time horizon is > 2 years)
Bitcoin is the perfect settlement base for layers built on top. The Lightning Network uses Bitcoin for its trustlessness and payments are also denominated in bitcoin.
I know that I sound like the typical Bitcoin-shill, but I really think that this is the one of the most important projects of our lifetime. It is the first shot at seperating money from power. Some of us just need to accept that we missed the early train and didn't get rich (we all would have sold at $200 if we bought at $0.30), but accept it for what it is. The first and only trustless, permissionless and decentralized monetary network.
I don't see the volatility stopping though. And being volatile upwards might be good for the spender who's been saving that money long term, but probably not for the seller who needs to count on that revenue to cover its monthly expenses.