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?
In the short term, no, I don't think it would be nearly as popular. Most of the outside attention that bitcoin gets has to do with its crazy price swings. "Bitcoin up 5 bazillion percent" headlines get people's attention. Without that, I don't think there would be much interest outside of those people who are already interested in cryptocurrencies.