Yes...stability does not necessarily mean serenity. The US and Soviet Union had a stable but stressful relationship for decades. By stable I mean, the two nations did not go to war with each other.
I doubt Xi and Putin want war with the US. The problem with that thinking is that wars are often started by mistake.
Kim Un, for example, might launch a test rocket that comes too close to Japan or S. Korea; so it's shot down. Kim Un thinks N. Korea is being attacked; so he launches against S. Korea and the US is there and involved.
China comes to the aid of N. Korea and now we, the US, are involved in a regional war with China, a nuclear power. NATO joins in as allies due to the attack on one means an attack on all provision of the NATO treaty.
Neither China nor Russia want an American presence on their borders, which would happen when the US smashes N. Korea; so now Russia joins China against the US. And Russia launches some ICBMs at the US.
Now we're in a global war, WWIII. All because the fat little dictator mistook the defensive action of shooting down a test missile for an attack on his country.