Yes, the vision is even more divergent than you accurately state. The USA has become a globe spanning empire, the largest arms dealer on the planet, and an oppressor of many less powerful peoples. However, to your specific question: a world without Lincoln? Do the times in which we live create great people? Is greatness thrust upon them? Or do great people somehow rise to the occasion and showcase their meddle? Without Lincoln, might another person risen to lead the USA in a similar manner? Lincoln was responding to tensions that were set in motion before the ink was dry on the Declaration of Independence. Without Lincoln, someone else might have done very similar things.
Then again, maybe not. Suppose the United States did indeed became untied. Slaveholding states became separate from the other states. Might either or both then sided with the Germany, Austria-Hungry, and Turkey during WWI? It was actually a close call anyway. The USA had many people who felt much closer to Germany than to the British. The British launched a massive media campaign to convince the US to join them against Germany. Whatever else, a divided USA during WWI might have meant that either (1) the Central Powers win WWI and (2) no humiliating treaty solely blaming Germany - which were key elements that gave rise to a mileau in which a Hitler type person could rise to power.
Interesting, because much of European Russia was signed over to Germany in the Treaty of Brest Listovisk (sp) in which Russia surrendered to Germany - ending the WWI on the Russian front. Germany, with its strong trade unionist movements, would become dominant in Russia, and the extreme communist elements might have failed to gain power, and more moderate German inspired workers unions would prevail (No Soviet grabbing of power nor a Russian civil war.)
Just my idle thoughts to your question. Any one else with a "what if?"