As an true naval amateur I will delve into the subject on a different tact maybe outside my real ability! So let us look at something other than the big three and ponder it from the lesser navies perspective.
First, I think carrier aviation is vey important in the first 20 years post-war, the aircraft are small, under performing, weak and we need a carrier to get any of the vital benefits they provide to scouting and spotting. Yes float planes can take up the task but initially that is sea plane tenders that do not really go with the fleet, especially in open water, and planes on ship tend to be a problem, either for fire, for recovery or what have you. Better is a fast ship that stays up near the scouting force to launch, recover and support aircraft. And with improvements the carrier can become the scouting force after that first 20 years of development work. Second, I think the other navies could make do, and might do better, with land-based naval aviation. Of the three (or more), France is the only one really even thinking of going that far from its land bases.
For me, only the USN and IJN are fighting in open water far enough from land to be divorced from concern despite Japan also innovating its RIKKO doctrine. Even the RN is operating near land everywhere, North Sea, Mediterranean, up the China coast through Singapore waters, etc. For the French, the Germanys, the Russians, the Dutch and especially the A-H navy, land bases are usually plentiful and well within range of a fleet at sea. For all of them the RIKKO strategy looks far cheaper, doable and successful. But even so, the carrier has its uses. So for anyone working in alternatives including Austria, Germany, Italy, the Dutch or even the Russians, I think a look at France might be useful. (And I include the many alternatives of a surviving A-H and German Imperial navies vaguely in the generalities).
I choose France because I think its carrier evolution is not entirely linked to the Treaty, is more focused to the role of aviation in battleship operations, and more applicable to the other navies, hopefully a less thought of but more thought provoking model:
France intended to build two modern Mediterranean “task forces” centered around modern, fast aircraft carriers--the Joffre-class--capable of operating 40 or more aircraft each, protected by new battleships of the Gascoigne-class (my guess is from 2 to 4 each) with the St Louis-class heavy cruisers following on from the Algérie, and the new 3900-tonnes Desaix-class destroyers, an improved Mogador “super destroyers”. The Joffre were about the size of USS Wasp. So with different aircraft somewhere up to 100 aircraft? And it appears the French were biased towards the strike mission, intending almost two-thirds the group to be strike rather than fighter aircraft.
Based on the above, despite seeking 8 to 10 battleships, the French were moving to the foundation of a carrier centric task force navy. And I believe from 1938 forward the carrier is going to have to be part of any battle group. It is now the center of the scouting force, it gives a better weapon to attrite an enemy battle fleet at distance, and if needed can fly more fighters to offset a land-based threat, likely more important as the 40s move on. Or this carrier centered task force could easily patrol the Atlantic, seek battle with an enemy task force in open water, or support the defense of a distant colony.
The French can easy fight Italy anywhere in the Med, it can also project into the Red Sea/East Africa theater if pushed. It could more easily contain A-H alone, or support Greece, or suppress the OE/Turks in re-plays of WW1 campaigns. It can at least go after Germany in the Atlantic, likely on equal terms given Germany's geography issues and likely inability to fully commit its fleet to beyond the North Sea and Baltic. France can certainly support its suppression of independence in its colonies but likely cannot truly defeat a serious Japan over sat Indochina.
So we can overlay that for Italy or Germany, the next more likely carrier navies. Carriers allow Italy to go beyond land-based umbrellas and seek battle with France deep into the Western Med, or threaten its position in the Levant, or actually project to the Red Sea/East Africa. An alternate Germany can now actually contemplate putting task forces into the Atlantic, against France that means the naval war gets real. Germany can also project force, albeit still likely far too little, to defend its colonies or its position in China, again not versus a top tier global or the biggest region power, but a carrier centered battleship task force becomes a genuine blue water naval arm for any of these lesser navies.
Without the Treaty we know the USA, GB and Japan are mirroring each other, likely more carriers, bigger carriers, better aircraft, more aircraft, and sooner. Japanese enthusiasts are already thinking aircraft not battleships are the decisive arm, land-based and carrier-borne are the new capital ship, and France shows that a carrier is going to be the necessary companion from 1938 even if you do not believe. So for the no Treaty world, the cycle should be an experimental carrier (or two), Langley, Ausonia, Argus, Hosho, etc., then a purpose built from lessons, two or more if you got the money, and lots of aircraft development. But before 1937/8 I suspect airplanes still look frightfully full of potential, only thereafter can we truly question who decides to gamble more on air than guns? I do not think we need the Treaty to loosen the grip of battleships of Taranto or Pearl Harbor to raise up the carrier, deeper beneath the surface the paradigm is shifting, even a smaller navy is going to need to have carriers and battleships before it can tap out of the race.