Nearly all those democracies have quota systems at the party level which dictate x% of women either running OR seated in the house (Depending on the Rep system); thesoleexception being Denmark (Which is an amazing anomaly and should be your case point, if this is the argument you're making). This COULD be, as you said, due to financing laws preventing the cabal of white males from controlling the parties and so these rock star progressive added quotas...Or it could be because in those countries, their representation, or election (Non-FPP), system makes it so parties often have to bend to marginalized power brokers; in order to avert dead locks. So small feminist factions have much more power, and quotas are a quick way to appease them.
Neitherof these answers work universally, because Europe has a pretty broad range of finance, election AND rep (Well, all parliaments but other variables) systems. However, I'd definitely lean more on "different types of democracy" theory more than the "cabal of white males controlling things"--for one reason; because money owns the politicians that it elects, if women could win the vote, those "white males" that control the parties would place women in there without a second thought (Yes, this is my opinion, take it how you will). There is no way these guys are going to risk their power because someone has a vagina; if the polls said X woman would do better, she'd be in, in a flash--and then she'd do whatever those "males" (Corporations) wanted, just like the men do.
Anyway though--within Europe, Only really in the Scandinavian countries were women making strides before quotas came into play; but even then, if I'm remembering right, they were still only hovering around 25-30% (The U.S. is about 20%?) The reality is, the Europeans have always been a lot less scared of "tempering" Democracy with rules that might limit choice (Limits a poor word, but this is already long) but make it functionally more efficient. The U.S. is pretty paralyzed in that regard, because we think even common sense changes will be the return of King George or something, meh. But for the most part, as Seb said, correlation does not equal causation. You can make the argument that campaign finance prevented white men from keeping control, and thus allowed quotas to be instituted. But you could just as easily make the argument that finance had nothing to do with it, and the "puppet masters" decided to toss in quotas because their election systems are so radically different that a confluence of factors made quotas an appealing choice.
