Past world leaders has shown otherwise
Not when faced with being blasted into the stone ages. Japan is the only nation that saw that as a real possibility; and they reacted accordingly.
No leader would want that, unless they were suicidal or mental. Even if Japan had nukes back then, they wouldn't have been interested in trading scores of nukes with the US. Same goes for the US.
If you fold every time I put you all in, you'll never win. Sometimes you
must push/call--no matter how scary it seems. This is why the US gets little respect from Russia/China. We're really just a super strong, but secretly scared, high school punk. Why?
Because that's what the citizens want us to be. This is why we will continue to be involved in dust ups with Russia/China whether it's election interference, IP theft, Govt. and Corp. espionage, Air space violations, Outer space violations, hacking, etc. etc.
Putin is currently showing otherwise
Putin is not facing the US right now. He is not attacking the US nor NATO. He has no need to worry about our nukes right now.
Likewise, China is not invading Taiwan/NATO. China talks shit about Taiwan; but talking shit doesn't count as 'facing nuclear war.'
The US is the only thing stopping them individually but if they form an alliance both will be willing to take on The US in an all out war imo.
Nuclear bombs from the US or other NATO members landing in their countries is stopping them, yes.
It wouldn't matter if China and Russia "team up;" Nukes would still land in their countries.
Only a mental leader would turn their country into a nuclear wasteland for no good reason--even if they formed a "team."
But there is no "right" answer, as we all can only offer opinions as to what leaders will, or won't do.