Most ancient apocalyptic prophecies of which I am aware regard the end of the world as essentially positive, if temporarily unpleasant. However, most contemporary imaginings of the apocalypse (which tend to skew more technological than religious) view it as something which must be avoided or overcome rather than as something necessary for the purification or renewal of the world. When and why did this shift occur? Were there ancient prophecies which had a wholly negative view of the apocalypse? Apologies if this treads a bit on the twenty-year rule.
My answer refers exclusively to the western/Christian tradition.
Apocalypse technically just means "unveiling" or "revelation." But the Greek word's preservation as the title of the last book of the Christian Bible in the Latin and early vernacular translations kept it very tied to the so-called 'last things,' whether that meant the Last Days or the death/judgment/heaven/hell quadrangle. In the early modern era, we can find a few references to secular apocalypse, as in the "revelation of Nature." But for the most part, it was religious, which is to say Christian. And since the early 12th century, "the apocalypse" had meant a loosely-biblical Christian vision of the coming End Times played out in our timeline.
The shift in meaning from the Christian end times, in which the devastation of the last days precedes the Second Coming of Christ, to a secular cataclysm occurs in the late 19th century. It's the first time that the West sees wide attention to "the future" as a development and extrapolation from the present state. In literature, we see this especially in the steam and electric-powered future of wonderful adventure and innovation in the American West.
The darker side is associated more, but not exclusively, with Europe: the "future war" genre, played out especially in invasions of England. Chesney's novella Battle of Dorking set the tone and Wells perhaps perfected it in War of the Worlds. Fear over the geopolitics of Europe and the implications of new weaponry and theoretical weaponry, along with a social shift towards valorizing soldiers, led many fiction authors to focus on war. This led to numerous popular portrayals of secular, martial cataclysm with no redeeming Christ on the other side.
But the first recorded reference to a secular, cataclysic apocalypse does not come out of proto-science fiction: it's from John Swinton's Striking for Life, which as the title indicates emerges out of the labor movement of the progressive era. Swinton writes:
In these times there are, as in other times there were, prophecies of the approaching apocalypse. It is not worthwhile to be alarmed, for it will surely come, and the world will rejoice in the new day.
This bit of amazingly-biblical rhetoric is, on the surface, explicitly NOT what OP requested. Swinton envisions a socio-political cataclysm with an ultimately positive outcome for the working class. But this is just the first recorded use, and I would argue it reveals how the understanding of "apocalypse" had shifted among his audience.
Swinton's apocalypse is unabashedly secular, and yet he is riffing heavily on the New Testament Gospels. He means to comfort a worried audience, awash in fears of "wars and rumors of wars" and social upheaval, by paralleling the situation to one that they know (or at least hope) has an ultimately positive outcome.
By the dawn of World War II, "apocalypse" had come to take on the metaphorical meaning we know of today as "disaster," with no promise of light at the end of the tunnel. Germany's descent into Nazism and the Nazis' rampage across Europe was referred to in the American press as the "apocalypse across the Atlantic."