I disagree that destroying a people destroys their culture.
One need only study Earth history to conclude that it is not that easy to "destroy culture". Heck, it's not even easy to actually destroy an actual people; they tend to live on among the new societies that arise, but their culture is usually stronger than the survivors themselves, because of the infectious nature of culture.
Besides that, besides the wishful thinking and the "logical" and historical aspects, culture-saturation has a gameplay use in this game.
However, I do believe that a new upstart colony needs some time of grace before succumbing to the permeating culture.
The way you, as a new colonizer, can fight this, is of course with more culture. Think of it as a multi-level game: You need to fight on the economical scale, then on the cultural scale, then on the military scale. One cannot simply air-bomb every problem that arises. Want me to cite examples from recent history?