NATO countries are very careful to not attack Russian forces in Ukraine. The main rationale given for this is "Russia has nuclear weapons. Attacking Russian forces might lead to a nuclear war."
Similarly, it seems that Russia is very careful to not attack NATO countries. One excuse for attacking Ukraine is that "it wants to join NATO", but other countries - which already jointed NATO - are not attacked. Probably, the rationale is similar: "NATO countries have nuclear weapons. Attacking them might lead to a nuclear war".
Now, suppose the USA (or another NATO member) invades Ukraine from the west, and occupies all the territories not currently occupied by Russian forces. Now, apparently, there is a symmetric condition: two occupying forces, both have nuclear weapons, both are careful to not attack each other in order to avoid a nuclear war. So the hot war will end. For Ukraine, this situation will be much better than being entirely occupied by Russian forces, so they might agree to this plan.
Is this consideration correct? If not, then where exactly the symmetry breaks?
NOTE: I understand that my "idea" is probably too naive, I just want to understand where exactly it fails. Why is this not a symmetric situation?