It is quite difficult to answer this question. If Bitcoin is having a stable price, then it will be popular with merchants and bankers. But at the same time, its attractiveness among the traders and the investors will take a hit.
Yes, investors and traders bitcoin will not be interesting, because they use it only because of a good price increase.
I think opposite, if bitcoin price stable. So will many long-term investors who invest money in bitcoin in a very large amount. And bitcoin could potentially be an international currency.
Can you give an explanation why so? Because investors right now are investing in hopes that the price of bitcoin will even go higher. If the price is stable, bitcoin cannot give you any profit regardless of how long or how short you hold your coins. For store of value, perhaps? I still don't think so because why would they put their money at risk like that when they can store their money in gold and other stuffs that have been around for so long and proven profitable.
Plus, it's actually impossible that something will have a stable price. Like in your example, if someone invested a large amount of money at something and it has a limited supply, then it will pump up the demand and increase the price.