What about corporatism, which is in some ways similar to fascism?I'll have to look it up. Thanks. After a look at Wikipedia: maybe. But planned economies don't work, hooray for competition (though in a free market there are some natural monopolies), and there's the risk of "too big to fail" corruption as well as corrupt labor (the old inefficient guilds; unions). Some say social democracy's failing; churchmen are a step behind, still trying to hitch their wagons to it.
As far as I know, Catholic social teaching is fine with any system or culture as long as, to use what I think is CST jargon, it is good for "the human person" and the church is free, state-backed or not; conditions for promoting human "flourishing." (I don't claim to be an expert and of course submit to the magisterium.) A baseline of universal rights, which are inherent, not privileges from the state (yes, I know, ironically this sounds like the American Declaration of Independence, by no friend of the church); a line of Catholic thinking going back at least to Bartolomé de las Casas. In any situation, nobody really owns the church, even when it's the state church; that's partly why the Communists hated it. They could and did take over the Orthodox locally (nationally), never us at the bishops' level (the church's basic unit, by the way). No Catholic bishop in Eastern Europe after World War II (the big Soviet victory) left the church when ordered to do so, as far as I know. Clergy have gotten involved in politics, right and wrong, but the church is apolitical. And CST's insistence on "the commonweal" (sound familiar?) is actually why the church has many "conservative" social positions (traditional marriage builds society) as well as "liberal" (most wars are wrong, as is selfishness). Socially conservative but moderately socialist (communitarian) economically is shorthand for CST; fits the old labor/Democrat Catholicism in America. (Freedoms and rights, yes, but responsibilities to your fellow man too.) I know in many ways Pope Francis isn't saying new things; Benedict the Great said much the same. (Like Paul VI, Francis' vacillations in the culture war are hurting the church. Note that nobody is converting from secular humanism to orthodox Catholicism because of them.) But churchmen's, even Popes', opinions on politics are just that, opinions. (I don't watch EWTN because I don't care; I have the traditional Mass and the catechism.) Another thought: you can argue that nationalism, as in falangism, is concerned for the common good in a way compatible with CST. Catholic liberals claiming to represent CST (and the dumb version, American nominal Catholic peer-pressure liberals) would recoil in horror at that but I believe it's true.
Catholic liberals, not to be confused with real Catholics, have been claiming that Vatican II agrees with "'reason' is WHITE bullsh*t," as if different practical solutions in different countries mean there's no objective truth. Actually they still believe in absolutes; it's just that they're ripoffs of the ones the church teaches (universal rights, etc.). Leftism is a Christian heresy; only a Christian culture could have come up with it. The council was really the church trying to put its teaching in space-age liberalism's terms, not change its teaching, which is impossible; it failed and actually hurt the church.
I dropped out of national mainstream American politics after 2000. I'd be fine with either a reset to the old American republic under a Ron Paul, the best of WASP America (we're not propositional; we're really still British) making a home for Catholics, or a caudillo.