Stable price indicates that either market is at complete equilibrium always which it can never be all the time. Sometimes demand will increase the supply and vice versa. This means that stability means no more booms in the market. Moreover it will take away livelihood from traders, arbitrageurs and hedgers, because no movement in price means trading closed Altogether and this will take away a big chunk of money as a lot of people are just to invest and make money.
the reason why many people are attracted on this market is because of the volatility factor of btc. if you remove this feature and btc becomes stable, yes, it may be good for payment method and other things. but the traders and other investors, will wane their interest and so this may affect the price. i don't think everyone wants a stable price. but less volatility may be favoured.