What would NATO gain? What could NATO do? The answer is because NATO shouldn't admit Georgia.
Should Russia have invaded? No, it is a completely disproportional response. However, the groundwork for these actions were laid long, long ago. Kosovo is what cemented this as well. You really thought that when the U.S. and the EU gave Russia the finger and pushed through Kosovar independence that the Russians didnt mean Georgia when they said they will keep Kosovo in mind with regards to regions demanding independence?
Russia baited the Georgians into attacking and were prepared to smash them if/when they took the bait. For whatever reason, the Georgians went for it despite the massive stupidity in doing so. It is a good bit of the West's responsibility that this occured as explained in the events above.
Remember, I dont think Russia SHOULD have done this but it seems obvious that this action, at least in part, is payback for Kosovo.
The problem then is that if we accept responsibility than one could say we need to act. What is it you would have the West do? Invade Russia? Deploy troops? Risk a near WWIII scenario over a small republic that acted foolishly? While honorable, in real-politik terms to react in that manner is the height of folly as the potential losses FAR outweight the gains.