Bitcoin would have been more popular and accepted by companies as a payment option if it had a stable price as they dont need to face loss due to fluctuation in price. But on the other hand, traders would not have liked bitcoin as now because they could not yield more profits due to its stable price. But for people who use bitcoin only for transactions would feel no differences if bitcoin had a stable price or not.
This is exactly what would happen. It would be very convenient as a payment option, but it's value as an investment asset will be gone.