WWI however it's not clear. None of the leaders of the big players took the assassination of the arch duke that seriously, nor did they care about Serbia all that much (it was a hotbed of tension for years as the Ottoman Empire was on the verge of collapse due to total lack of interest in reforms by it's leaders) so it was not that surprising.

You'd be wrong here; Austria-Hungary's leaders took the assassination very seriously, as Hotzendorff and Berchtold in particular had been set on a reckoning with Serbia since 1913, when the Second Balkan War ended.

As they all got drawn in to the conflict due to alliances, even a quote from the Kaiser basically saying that if Queen Victoria was still alive this would never been allowed to happen (pretty much every Royal in Europe were cousins at the time) reinforcing that there was no real animosity between the nations.

This again is wrong. Austria-Hungary went to war based on it's own interests in the Balkans, and because the Germans had agreed to support them. The Triple Alliance was defensive, and did not come into play here, hence why Italy didn't join. Russia and France both had war declared on them by Germany, whose own leaders had been preparing in earnest for a strike against the Entente since at least 1912. Finally, Britain stepped in when Belgium was invaded. The Alliances didn't come into play, for if they had then they could have deterred the actions that followed. Instead, Austria-Hungary and Germany pursued their own policies, and this lead to war. And considering that there had been an arms race in Europe going on before 1914, I don't think I would take the Kaiser's word of mouth as gospel.

So after the initial "romance" of war wore off, and the real business and horror of war was in full effect, why did it continue? What was the end goal? Why was it not just sort out Serbia and area and then deescalate? A war that no one wanted, no one cared much about that became the most widespread and violent event up to that point makes no sense to me.

There wasn't "romance," and even if there was it was only held by a segment of these populations. Socialists were familiar with the writings of Engels, Marx and Bloch, which depicted war as a catastrophe, and one that was a result of capitalist interests. Norman Angell, Alfred Nobel and Bertha von Suttner took up similar lines of argument from a Liberal perspective, while even conservatives like general Colmar Freiherr von der Goltz argued that wars of the future would be "People's Wars," and would be long and bloody.

Although few could have foreseen accurately how the war would play out, a long war was very much seen as being in the cards, and there were those who had pushed for war before July 1914. For Moltke, Kaiser Wilhelm and others at the Wilhelmstrasse, this was an opportunity to break the 'encirclement' of the Entente under favourable circumstances. Likewise for the Austro-Hungarians, it was an opportunity to finish off Serbia and secure the future of the Empire. The British had spent almost a decade since 1905 trying to restore some semblance of a balance of power to the continent, and now this could only be done by subduing the Central Powers. And of course, for the French and Belgians this became a war to defeat Germany, and end it's occupation of their homelands. There were reasons for the Great Powers to have gone to war, and it was not as simple as "sorting out Serbia" when the fortunes of war were so uneven from the start.

Your question might be answered well by considering that for each of the opposing sides, the war reached critical mass very quickly. You point out the destructive nature of the war. This is the very key to its continuation.

The most destructive wars that Europeans had a collective memory of (the Napoleonic Wars) resulted in somewhere between 2.5 and 5 million military deaths. Much of which occurred in the later periods of the war and this was over the course of a 12 year period. In the first three months of WWI, roughly 270K+ had died.

Hence, we can see that the war was immediately devastating and yet none of the sides had delivered a devastating defeat. The Germans were on French soil, but the Allies still had strategic and numerical advantages. In the past, such a situation might have led to a peace treaty with small dynastic territorial changes (or none at all), but this could not be the case in WWI for a couple of reasons.

First, Britain was ostensibly in the war for reasons other than territorial changes. It is tough for a democratic society to sell high losses of men simply for a few pieces of land. The dynastic powers could certainly do so, but such was becoming less and less popular as populaces began to express themselves more. As war became a greater undertaking for an entire state and not just a monarch, the reasons for war were changing.

Second, the losses incurred necessitated some sort of compensation, but the high level of those losses meant that the compensation would by necessity have to be heavy. With neither side having been defeated, who would pay this compensation? Neither side was willing to make the payment and neither side was willing to have lost all those men for nothing.

Finally, the war propaganda was such that at least to some degree (historians debate the influence of the propaganda) the peoples of the opposing states viewed their opponents as barbarians. The Germans depicted the Russian hordes. The British played on German atrocities in Belgium.

There are other reasons that the war continued such as the nature of the alliances, continued radicalization of war aims, internal politics, and brinksmanship. However, to fully discuss these would be quite a task. Feel free to ask more questions though.

TL;DR

Due to the high loss of life in the war, none of the governments could leave the war empty-handed. Otherwise, those lost lives would have been meaningless.

Sources

Gilbert, Martin. First World War. London: Weidenfeld & Nicolson, 1994.

Keegan, John. The First World War. New York : A. Knopf, 1999.

Marshall, S L A. World War I. New York: American Heritage Press, 1971.

Germany's entire strategy for the war was to quickly take out France so that she could then reallocate her resources toward dealing with Russia. If she hesitated, or so her military planners thought, she would lose her key advantage - mobilization speed.

Germany could swarm troops into France before she mobilised properly, while Russia was expected to take up to six weeks to mobilise her forces. If peace deals were made and then broke down (while France and Russia were preparing for war), Germany would ultimately find herself trapped between two massive forces and the weaker party in negotiations. As far as the German military was concerned, She had to go, and she had to go immediately.

Ultimately, it didn't work out entirely as planned - Germany was able to not just hold off the initial Russian assault on her eastern flank, but decisively defeat it at Tannenberg. While the French were able to survive the initial German onslaught and then launch a counterattack.