What allows historians to combine the various religious wars in the Holy Roman Empire at the beginning of the 17th century into the Thirty Years War, but prevents them from combining WWI and WWII into a similar grouping, despite both conflicts being fought over a similar scope of time, and each maintaining strong ties from the end of the first war in the "period" to the motivations for the second?
In fact, the Second 30 Years War formula has been used, by no less a figure than Charles de Gaulle, as a way of minimizing France's catastrophic loss in the Second World War by conflating it with France's heroic struggle in the First. Henri Rousso's Vichy Syndrome, a book about shifting attitudes about Vichy since the war ended, argues that de Gaulle saw this formula as a recipe for national healing.
The "WWI/WWII as a continuous conflict" aspect of your question has been discussed here here and here.
/u/Restricteddata proposes what I think is a very reasonable test. Is it a useful categorization? Does it help explain or foreground factors that are unexplained or un-examined in the conventional two-war model?
Or on the other hand, does it de-emphasize salient points and introduce lots of complications that need to be explained away?
Now, in my opinion, the "continuous conflict" categorization introduces many many complications that need to be explained. For instance-
If British, French, German, Italian and American armies aren't mobilized and shooting at each other from 1919-1939....isn't that peace? How is it a Thirty Years War when there is twenty years of "truce" in the middle?
What about the various peace treaties such as Versailles, Sevres, etc. If those treaties had the stated aim of ending the state of war between the contending powers, what reason do we have to believe that a state of war still existed despite what those treaties say?
Where does the Russian Empire fit in? it ceased to exist in 1917, to be replaced with the Soviet Union, Finland, Poland, Estonia, Latvia and Lithuania. From 1939-41 the Soviet Union and Nazi Germany had a non-aggression treaty and economic development partnership.
Where do the Austro-Hungarian and Ottoman Empires fit in? They ceased to exist in 1919, replaced with many independent nation-states.
Where does the Weimar Republic fit in? Was it actually in conflict with UK and France from 1919-1933, when it interned the High Seas Fleet, and was paying war reparations?
Where do Italy and Japan fit in? From 1914-1918 they opposed Germany, but 1939-1945 they were in a military alliance with Germany?
Does categorizing it as a continuous conflict over-estimate the inevitability of the rise of Hitler (and Mussolini) and under-estimate contingent factors like the Great Depression?
What is the essential character of this Thirty Years War? Is it fundamentally a conflict between successive (Imperial-Weimar-Nazi) German regimes against Britain and France (and Russia/Soviet Union)? Doesn't that de-emphasize perspectives from outside these great powers? Would that make Poland's national history from 1919-39 a footnote in the Thirty Years war? Isn't that Eurocentric, ignoring the conflict in Asia from 1935-45, or saying it is just a footnote as well?
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From my perspective, all of those questions are adequately explained by the current model, and I think calling it a "Thirty Years War" would make those questions more woolly, not less.