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.
Then, why investing in bitcoin instead of fiat in which have the same stability but fiat have advantages of backed up by the government and widely accepted without that much risk which ibitcoin investor bear?
Investor/trader will definitely prefer fiat and gold because it's also recognised officially by the local government, bitcoin might be banned, but these two will always be accepted and will always be for another century.
And be honest, an international currency without the recognition of the major country is nothing.