Is it not possible that it would be preferable to both sides, even in a hot NATO-Russian war to stick with conventional weapons?
Russia just wants Lebensraum, which would be ruined by nukes, and NATO would probably not want to seem excessively cruel to Russian civilians when their purpose is supposed to be entirely defensive.
Testing something like this is dangerously close to the brink. It's highly unlikely that the losing side would agree to lose without using their most powerful weapon, and it's highly unlikely that NATO would wait for a Russian first strike, which they would likely believe very possible, especially given all the demonization of Putin and Russia.
Don't forget that there have already been numerous close calls in terms of nuclear war, without anything close to a conventional war as background.
Russia just wants Lebensraum, which would be ruined by nukes, and NATO would probably not want to seem excessively cruel to Russian civilians when their purpose is supposed to be entirely defensive.