First, there are countless other ways to get Europe to rearm if that was actually the goal. Russia's position at the moment is virtually the same as it was a few months into the invasion, which is strong enough that european powers are scared of escalation but not strong enough that anyone thinks an unprovoked Russian attack on NATO territory is either imminent or inevitable. Making Russia weaker to lower fears of retaliation or letting Russia steam-roll Ukraine would both seem like they would better motivate Europe to quickly rearm instead of pressuring for a ceasefire.

Second, it is not at all clear that was the goal. Note that this is extremely against America's interests. As the major supplier of arms to Europe, America wielded tremendous influence over Europe (as evidenced by TFA) while at the same time ensuring Europe was well armed with weapons that would be easily compatible with the US's own military so that they could be readily called as allies. Europe replacing American systems with others does not mean Europe will be militarily stronger, it only means they will not be reliant on the US for what strength they have.

Third, there is no reason to believe that Europe would not feel compelled to build up military capability against China for exactly the same reason the US does. Nor is there any reason to believe China is too smart not to play into America's hands while Russia apparently is. Further, the US doesn't need Europe to rearm for a war with China - even with massive investment, Europe is not going to have the force projection capabilities to support a total war in the Pacific theater, what America really needs is a coalition of economic allies which will side with it in containing China - a need that is not at all served by antagonizing those very allies.

That's not to say any of your assumptions can't be true, just that it's a lot more assumptions than just "the current American leadership is not working to advance the American hegemony."