(Neo)/Realists like Mearsheimer and Waltz laid down pretty conniving arguments that the end of the Cold War and the concomitant fall of the bipolar international order, would result in balance of power problems that would lead to war/conflict.
They say states are much more secure in these bipolar systems compared to multipolar ones, so my questions is why haven't we seen WW3 or other conflict? Is nuclear deterrent still the primary reason?
Due to the rules of the subreddit, I can only comment on the period from 1991 to 1994. We don't discuss anything less than 20 years in the past on this subreddit.
There actually was quite a bit of conflict in the wake of the Cold War. The 1991 Persian Gulf War occurred at the end of or soon after the Cold War, and it was a major war in the Middle East. The wars that came with the breakup of Yugoslavia killed over 100,000 people. Likewise, the Soviet Union's collapse led to some very bloody wars. The First Chechen war, the Nagorno-Karabakh War and the Georgian Civil War were all very bloody.
Major power conflict was avoided because there were no comparable military powers to the United States and NATO in the Atlantic, or to the United States and its allies in the Pacific. The Persian Gulf War had shown the world that the United States was without peers in terms of military power, as it had defeated a numerically superior opponent halfway around the world on their home turf. The main power that backed other nations that opposed the United States, the USSR, had folded, and with it folded the free arms, military advice, protection, and economic goodies that came with its hegemony over most of the Communist world. China had few disputes with the United States, and while it had a large military, it was not terribly advanced or well funded by today's standards.
Nuclear deterrents may help keep full scale wars between great powers for happening, but I personally believe that part of what kept the world stable in the wake of the USSR's breakup was a demonstrated willingness by the USA to involve itself militarily in conflicts that didn't directly affect it militarily. Iraq in 1991, Somalia and Bosnia in 1994, and the war scare on the Korean Peninsula in 1994 showed that outside the former Soviet Union, any sizable conflict ran the risk of United States intervention. Moreover, no nation in the world at that time was capable of defeating the United States in a conventional military conflict.