It WILL violate the 'stoneness of time' as you put it, if they only get rid of the machine and ignore Ultimecia. Because Squall HAS to fight Ultimecia and defeat her, so that they can both go back to the orphanage so that Ultimecia can pass on her powers.

Furthermore, the machine was needed for TC only indirectly. TC had some sort of requirement which meant Ultimecia had to be in the far past(relative to Ultimecia) to cast it, and the only way to get to the past was via the JME. However, once she had cast the spell, JME no longer has any significance. An analogy: you have a bomb, but the detonator key is in another location. So you use a car to get to the detonator key, and then blow the bomb up. However, the bomb is not in any way dependant on the car! The car was just the way to get to the location.