World War I would be very hard to avoid, considering most nations were just waiting for some kind of crisis to happen, so the war could begin.
Not true. There were some military jingo types, but most everyone else quite rationally considered war to be a probable calamity.
Germany, Russia, France and even Britain were looking for a Casus Belli.
Germany, yes. Russia no. Russia had just gotten beat up in the Russo-Japanese War. France no. They knew Germany outweighed them. Britain no. Britain had no interest whatever in war with any Continental power. They preferred making money.
Turkey no. They had been crushed in the Balkan Wars. Italy no. Too weak to challenge anyone else. Austria-Hungary no. At most they wanted to use force to crush Serbia. Most A-H pundits and intellectuals worried or hoped that political collapse was imminent, and a war would only bring it on.
Especially the Germans thought they needed to start a war soon,
Some Germans. But even as big a jingo as the Kaiser flinched at the brink in 1914. I don't think there was a majority for just going to war; the war situation had to be ginned up.
the Great War just don't happen. What happens to the nations and empires of the world in such a TL.
Massive political crisis when the Ausgleich comes up again, especially if FF is in power instead FJ. How it boils out is anyone's guess, though I would expect that a truncated Empire may survive.
Continued economic growth. At some point pressure for political liberalization becomes irresistible. The Kaiser lived to 1940, and he's incapable of compromise - but it may be forced on him.
Some level of internal reform. The monarchy staggers on. Arab nationalism may start to disrupt the Asian possessions. I don't think there would be a massacre of the Armenians. Russia would intervene, with world approval, and the Turks know it. Turkey does not get the sort of drastic shake-up Kemal imposed, so it remains backward - but it doesn't get the smashing that it got it WW I either. (Turkey had the highest proportion of military dead to total population of any belligerent except Serbia.) That's got to help.
Rapid economic growth, but serious political problems due to Nicholas and the camarilla. Further democratization may be demanded by 1920 or 1925. If Alexei succeeds to the throne, his illness will weaken the monarchy. (Even Bolsheviks may feel sorry for him, but the system has put a manifestly unfit person in power.) No Revolution for quite a few years.
An immediate crisis over Home Rule in Ireland, which OTL was defused by Irish Nationalists saying they would wait till after the war. (Which ultimately killed them; the Irish Republicans rose instead.) The government could pass a Home Rule bill, but Ulster Unionists threatened to oppose it by force ("Ulster will fight, and Ulster will be right!") There were threats that the British army would not enforce Home Rule (the Curragh "mutiny"); there was even talk in some Conservative/Unionist circles of extra-political action in Britain.
Idunno, but almost certainly no Fascism.
Millions of men not killed and land not ravaged. Economic growth?
Wilson may not be reelected in 1916. (TR the warmonger was an albatross for the GOP OTL. In peacetime, not so much.) There will not be a war-export boom in the US. The massive program of economic controls created by Wilson for the war won't happen, nor the extravagantly nationalistic propaganda campaign and war hysteria generally. No American Protective League chasing down defeatists and sedition. No Red Scare. Possibly no Prohibition - ISTM to have been sold in part as a wartime efficiency measure.
The U.S. having avoided involvement in a hugely disappointing overseas war will not dive into Isolationism in response. If there is a major world crisis further on, the U.S. could get into it.
Japan doesn't acquire Micronesia. The drift toward militarism may continue.
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Other critical things.
The Battleship Race - how long does it continue?
ISTM that at some point, countries are going to get tired of spending huge sums on battleships that never get used. This happened in the early 1920s, and may happen earlier. The Kaiser may be an obstacle.
China
OTL, the disorder after the Chinese Revolution happened while the Great Powers were all busy with the Great War, or its aftermath, or when they were exhausted or beaten. ISTM that if Europe is at peace, the Powers will be much more likely to intervene in China. Japan of course was
not affected by the War; I don't know how much Japan meddled in China, or wanted to; but Japan is much less likely to get its way.
Them's my thoughts.