WWI and WWII can be seen as one war, which was the attempt by Germany to displace the UK and wider Anglo world as the dominant western power. I think it makes sense to group the wars together.
Not very widespread. You may not have a very long view on history. Take a look at my username (I'm "English" by the way). Just in case I need to spell it out: Gerdes ~= German.
Those two wars had very different reasons despite Germany being a participant in both of them. Russia (famous for not being Anglo) was a major player in those wars as well and we should not overlook Japan etc as well.
WW I is the more important because it destroys the power of the royal families that ruled the empires of Germany, Austria-Hungary, Russia, Turkey and China. By the end of WW II most royal families were reduced to figurehead status, except for the British and the ones that Britain tried to re-establish in the Middle East.
Yes, I really like the Thucydides trap framework, but this perspective must be seen from the PoV of the current hegemon. None of the Axis powers wanted to fight the US or even Britain, but the Atlanticist hegemon saw the development of Eurasian powers as unacceptable and must be put down.
