England, France, Israel... They all had nukes the entire time. What you are claiming sounds good but does not align with reality. You are overstating both the degree to which things have changed as well as overstating the degree to which the alliances have changed (i.e. Europe is still Europe. Poland won't be arming itself to protect against Germany or France, etc).
Now every actor needs to have the strength to deter all others, which means everyone gets stronger, which means everyone needs even more strength to deter others, or deterrence simply breaks down. We had a multi-polar world in the past, it went terribly and led to massive wars. Now we are returning to that system but with nukes.