Do you think if BTC had a stable price which could only be altered by $0.01-0.10 it would still be as popular and as used?
It will become more popular, because larger organizations will consider to use Bitcoin to transfer payments and won't need to worry about daily price fluctuations.
It can of course, at a constant interest in Bitcoin price remains at large organizations. But people have lost interest in this.
I don't think people would lose their interest in bitcoin if the stable price will happen, maybe only a certain portion of the group will lost its interest in bitcoin as they will no longer earn by doing day trading, they will surely miss the big price fluctuation of bitcoin.
Exactly they would switch to other coin which has more volatile price and traders would like that and its not only a small portion because big investors do also like on bitcoin because of moving prices and if bitcoin would stable its price then popularity would somehow decrease.
It could possibly happen, if whales trust the new coins they would definitely put money on it and us being a member here in the community we will just follow where the money at, maybe that time we can see a more progressive different coins from altcoins.