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?
No. I dont think that if bitcoin had stable price then it would have been this popular and users. This is because then there was no difference between banks and bitcoins. The matter of fact that people go for bitcoin over banks is its instability because of which its price fluctuate and have a high chance of increasing resulting in increase in your invested money. So bitcoins biggest weakness is its biggest strength which is it being not stable and not regulated by any government. Which has lead to its increased popularity and users.
The price fluctuation, the value and the function of Bitcoin are the reason make many people want to buy it.
If Bitcoin price become stable, no one wants to buy more for investment long term because Gold will be better than and safe than Bitcoin.
In that time, Bitcoin can only be useful for international transfer money.