^ The Russia example was referring to the socio-economic collapse of the old Soviet Union, it's not quite the same as post Dominion Cardassia but it does show that a society can make a full recovery (or at least to a limited extent).
Japan is a major power, their economy was strong and they have recently began to update the JDFs. It's still one of the top industrial nation states (despite the economic downturn). I would not judge a major power solely though it's strength of arms.
As for Nuclear weapons? The Japanese have a cultural aversion to nuclear weapons for some reason.
Power structures change, the Germans became an economic and industrial powerhouse as a result of the second world war. It's not a world power because thankfully European colonialism is dead.
To get back to DS9, the Cardassian Union died at the end of the war anyway what I'm talking about is the society that will follow it.
The AQ powers were fighting for their freedom not to conquer Cardassia, they had to plan an invasion of Cardassian space because it was Dominion territory with all the bases and resources that they needed to persecute the war.
However the actual point you were making was about the status Quo, I don't think that will ever happen. The Cardassian homeworld is devastated, millions of soldiers have already died in the war and the Government of the Union has collapsed. There's no way in hell that the Cardassians will ever engage in empire building for the next few decades, if ever.
Their fleet (or what's left of it) would probaly be used to guard the core Cardassian systems with the exception of the formerly occupied worlds of the Union who would either join the federation or go independent.
I say the Federation quite deliberately as they seem to be the predominant power in the AQ. They proved aid to worlds outside their own territory (including many Klingon worlds no doubt) and I think they would have the final say in what happens to the cardassians.
The Klingon Empire suffered major casualties in their civil wars, the wars with the Cardassians and the Federation and of course during the DW itself. To be frank how THEY can remain a major power is a mystery also.
I think that there would be a short time protectorate of the ex-Union but I doubt that the AQ powers would be able to maintain it for long especially as the Cardassians would be too weak to start any wars for a very long time. So there would be no permanent need.
(And massaging the Klingon's pride is NOT a good reason to occupy Cardassian worlds IMO.)
The Cardassians no longer have the industrial base to build 'fleets' of
'Galors' but they would maintain a military to defend themselves from attack and pirate raids. The Cardassians would need to make a treaty with the allies allowing for this measure of course.
And Tribbles with their own Empire
Did they HAVE to join the USA or did they chose to help set up an independent international organisation dedicated to the prevention of another world war, AND maintain their militaries in a defensive role? 
