[Do you believe Georgia is in the essential interests of the US?
Is their territorial integrity worth a single US life?
How about a US city?]
The real question is whether their expansion is worth a single Russian life or a single Russian city. Because it will come to that eventually. Russia is not a band of nutty, incompetent religious fanatics - it’s a world-conquering power with a long record of successful acquisitions. In the long run, we will either stop their expansion or be conquered by them.
Czarist Russia took Siberia from the Chinese after they lost the Crimean War. Vladivostok actually means 'Eastern Fortress'.
And the Chinese are taking it back. With Putin smiling the entire time.
Russia's population crashed when the Soviet Union did.
Worse, emigration of actually skilled Russians gutted their tech programs (And still does).
And Russian, ummm models, are a fixture across Asia in their red light districts.
Those statements, while mostly true, do not explain what interest the US has in preventing Russia from doing as they please with Georgia.