You might first ask, “Why does any religion exist?” Existential comfort is probably the briefest explanation as Xanthippe explains.
People want some certainty in a changing world and people want an explanation for why things are like they are. Explanations might satisfy emotionally but they need not be true. Most people who use rational thinking e.g. in the world of academia, conclude that there is no need to invoke spirits, gods or magic to explain our universe.
So down to the specific question “What is the reason that JWs exist?” I would suggest that it is due to the efforts of entrepreneur CT Russell and the fact that his Watchtower outfit had commercial success; an understandable event considering the religious appetite of people in the US at the end of the 19th century. Secondly, that JF Rutherford, after great membership loss, was able to print 400 million pieces of brain numbing literature at a profit to make the Watchtower rich. However under NH Knorr the biggest source of wealth was the impetus given by declaring the doomsday year 1975 which accelerated membership numbers and yielded a vastly larger income platform as a consequence.
What then is the major reason they exist? It is because they have a history of successfully deluding millions into a false belief of a reward of paradise if you comply with the demands of the JW org-- and making billions of dollars from it. Who but an honest moralist would bother to kill such a productive cash cow?