That's a very good point:
Here’s the lame narrative that’s animating the Bismarck wannabes: The United States is pushing back against Moscow and pressing Beijing. This is driving Moscow and Beijing closer together. Beijing and Moscow will then gang-up on the United States. To prevent this, the United States should make nice with Moscow (undermining the incipient Sino-Russian détente) and then focus on beating back against China.
As I've argued, Russia needs America far more than we need Russia:
Really, Russia (and European NATO states, of course) and not America has something to gain from peace between Russia and NATO. The question should be what Russia can give to NATO to get peace so Russia can deter China from invading and liberating portions of the Far East that Russia took from China in the 19th century.
Let's not throw away our bargaining position with Russia. We don't need to offer concessions to Russia for Russia to try to avoid getting hammered by China.
So work the friction between China and Russia even as we work to resist both, rather than try to charm and bribe the paranoid Russians into friendship with America.
The Russians won't come to us until their nuts are in a Chinese vise. The Chinese won't let us down.