Actually, in the book, it does take decades (two, I believe) before the Nazis show their fangs and turn on the Japanese. Before that, the two powers proceed in a faux alliance not at all like the Cold War.
Of course, the book does posit near-domination by the Axis, with the US occupied by the Nazis along the Atlantic and the Japanese along the Pacific, with the besieged Central States "free." Not an entirely accurate extrapoloation, I grant (for one, Imperial Japan is depicted as way too benevolent an occupying force) but a damn fine novel just the same.
I think that a Cardassian-Romulan alliance would have to plan on a long war, too (not to mention some very difficult occupations). They, too, would have to contend with large areas (interstellar in their case, so "large" is putting it kind of mildly

) that would be difficult if not impossible to bring under their dominion.
(Oh, and thanks for mentioning
The Man in the High Castle - I've never read it but I've always meant to.)
Praetor said:
If they could trust each other long enough, they would probably take the quadrant.
Take it? You bet. My question is...would they be able to keep it? Keeping it would require a continuing trust or pragmatism or
something that I'm not sure either side has, something that would not only bring them together for their mutual benefit but also keep them together once the immediate benefit has been achieved. Ooh, tricky!
I think that might actually be a apt RL example in terms of the Geographical distance between the CU and the RSE so I'll forgive you for making it
JustKate.
(obviously I'm not in favor of the Cardassians as 'space Nazis' or the Romulans as either Fascistic or Maoist and I don't see my hypothetical alliance as the 24th centuries answer to the Axis powers of WWII. So there.

)
That's exactly what I had in mind - the distance.
But while I, too, am not in favor of putting either the Romulans or the Cardassians in some tidy little 20th-century-Earth ideological box, there is another similarity as well, one that struck me even more than the distance. The thing that neither the Imperial-Nazi scenario nor the Romulan-Cardassian scenario addresses is the mutual
loathing that the allies in each case would have for each other. For Japan and Germany, it was out-and-out racist loathing, bred almost to the bone - and it's impossible for me to imagine that would have ever gone away so long as the Third Reich and the Empire were around to reinforce it. Each literally considered the other group of humans less than human, but they were willing to put up with each other for the sake of their respective empires. For a while...
For the Romulans and the Cardassians...well, it's harder to say. It's difficult for me to imagine two such practical and pragmatic peoples despising each other out of simple bigotry...but then, it's hard for me to imagine the mindset of the WWII-era Germans and Japanese, either, and that is a world that I know from first-hand reports. It seems to me that xenophobia and contempt for any other species is bred pretty well to the bone in Romulans and possibly in Cardassians as well. So I suspect that such an alliance would work long-term only if something fundamental changed in, particularly, the Romulan psyche. Which could happen, don't get me wrong. But I think any scenario that considers Romulus and Cardassia taking the quadrant and keeping it would have to address this issue. It doesn't have anything to do with disrupters vs. phasers or cloak technology, but it's still crucial, IMO.
My analysis of the situation runs as follows, as the Cardassians and Romulans are both a highly pragmatic peoples they would use the alliance for specific and achievable goals, for example containing the Klingons within their borders or effecting regime change. Although the RSE has very nearly succeed at this several times before it would be more beneficial to have an ally that could...distract... third parties and use their own resources to enable for a speeder resolution.
That's just one notion that I've had, I'll post some more up later and address some of the interesting points made in this thread.
(I will not be able to do so in this post because ironically I lack the temperament for long winded posts

)
"Distract" is very good - the perfect word, if I may say so. Cardassians would definitely need to take heed! And I agree that having specific and achievable goals would be the key. When it would get tricky is after those were met.