I think what you're describing is that the American Civil War was between an essentially internally-unified central government on one side, and a union of essentially internally-unified local (state) governments on the other.

Many of the other civil wars you describe involve either a split within the central government itself, or a popular uprising with none or very limited support from existing government structures. In these cases the nations in question are more vulnerable to wholesale government collapse than the former.

I think the cases like the American Civil War are only rare because usually these conflicts are not classified as a 'civil war'.

For example, the Dutch Revolt was very similar to my description of the American Civil War above. You had an internally-unified central government on one side, and a union of essentially internally-unified local governments on the other. But we do not call it a Civil War because.... that's really open to debate.

I'd say basically because the Dutch won so we now identify Spain and the Netherlands as two separate nations therefore the war between them was not a civil war. Had Spain won and the nations remained unified since then, we'd call it a civil war (would never have happened considering the geographic and cultural distance, but just for the sake of argument).

I think what it just comes down to is the by definition Civil Wars are a conflict within a nation. And it requires a special set of circumstances for the fault lines within a nation to fall so neatly amongst administrative lines that both sides are able to set-up separate functional governments.

Also, as an aside, you add the English Civil War to this list. I am not familiar enough with the period to authoritatively refute this, but afaik you really can't argue both sides had organised governments controlling stable territory that meet the definition of a state. Again afaik, there definitely was a breakdown of central authority in this period, just not a very major one and the relatively quick Parliamentary victory prevented it from becoming so.

Does this pattern actually exist and, if so, why does it?

I'm not convinced this pattern actually exists. The War of the Roses was an English speaking civil war with all the characteristics you described:"competing factions which barely overlap, and often lead to the rise of warlordism, often accompanied by the collapse in authority of the central government".

Conversely, there are several examples of non-English wars with two organized, legitimate (sort of) governments both fielding armies with a proper chain of command. Look into the Roman Crisis of the Third Century. The Roman, Gallic, and Palmyrene states all meet these qualifications.

If this war is too far in the past to qualify your consideration, the Korean War may be a better example of a recent civil war with two organized states fielding proper armies.

Well, I will note that the three English speaking civil wars you name as examples all happened before the 20th century. On the other hand, the Spanish civil war happened in the 1930s, the Congo Crisis and the Simba Revolt happened in 1960-63 and 1965-66 respectively, and Liberian civil war happened 1994-2003.

Rather than looking for a cause rooted in Anglo-American culture, I would propose that the differences are rooted in the changing nature of conflict in the 20th century. Particularly, the intervention of Great Powers or Superpowers into civil wars, thus making them in some aspects a proxy war between contending powers, as well as prolonging the duration of the conflict.

To again look at the Spanish Civil War, it has numerous examples of foreign interventions. Germany and Italy sent pilots and aircraft to support the Nationalist side. By the same token, the Soviet Union sent arms and materiel to aid Marxist elements within the Republican side. From a different end of the ideological spectrum within the Republican movement, the war saw volunteers from across Europe and North America take part, including the American Lincoln Battalion.

In the Congo Crisis, this trend of foreign intervention is also present, be it as Belgian mining companies and European mercenaries supporting the Katangan and Kasaian secession, or Western fears about Patrice Lumumba soliciting aid from the Soviet Union. Or even UN armed forces going in to support the government in Kinshasa.

Again in the Simba uprising in the Mid-1960s, you see Chinese supply of arms to the Simba rebels. Or in the 1970s during the Shaba invasions, you see Moroccan and later French and Belgian intervention to support Mobutu's government against Katangan rebels supplied by the Soviet Union and operating from bases in Angola.

Now, to bring the analysis back to the English Civil War, the American War of Independence, and the American Civil war. In the first and third of those wars, there was not that much international intervention in the conflict. Granted, Scotland and Ireland did play a role in the decision of the conflict between Royalists and Parliamentarians, and Cromwell did conduct campaigns in Scotland and Ireland after Charles I's execution.

If we are defining the American War of Independence as a Civil War, which we will for the sake of argument, then it must be admitted that there is a considerable amount of foreign meddling in the conflict. This comes in the form of Spanish financial aid for the American cause, French arms and men, and the Dutch opportunistically declaring war on Britain as well.

But, on the other side of the coin, the American War of Independence at some points was not quite so neat a conflict as you describe. The conflict between Americans and Native American nations allied to the British had little to do with ideals of Taxation, representation, or loyalty to King and empire.

So, to more clearly state my point, the American Civil War seems so different from others you mention because it did not see much foreign intervention in it at all. As a broad rule, civil wars since 1945 have tended to see much more involvement from foreign powers, and until 1990 intervention was often motivated by Cold War competition for influence.