...but it's not like most places in Europe are doing so great either. And I'm at least semi-convinced by the argument that America's particular distribution of crazy opinions would end up leaving the government in a very bad place under a parliamentary setup.

I've been toying with the idea of going in the other direction and just trying to cripple all political parties entirely. Obviously you can't prevent politicians (or voters) from forming whatever associations and private clubs they want, but...there's a lot you could do to prevent those associations and clubs from being in any way relevant. Make it unlawful to put party affiliations on ballots. Stop having publicly-supported primary elections. Change congressional procedure so that parties can make many fewer decisions and control many fewer things.

(And none of it would even require changing the Constitution!)

a particular application: most far-whateverism sympathizers are only sympathetic to certain specific goals and principles, not the whole construct with its associated conspiracy theories etc.

Against this, you have to consider that most of the people who are knowledgeable about a given industry got that way by working in it.  Excluding them for fear of perceptions of corruption will tend to narrow the pool of expertise.  Moreover, you probably don’t want all of the regulatory shots called by people who’ve never been on the other side of the regs.  Everyone is generally in favor of rules they never expect to have to obey themselves.  This is true even as our own personal experience with compliance tells us that regulations are often ill-considered, unduly burdensome, or superfluous to anyone with common sense and decency. 

(I’ve worked as a carpenter and as a grad student.  In the former job I ran around all day wielding things you see in horror movies.  In the latter I sat around all day behind a keyboard.  Guess which job had way more regulation?)

But It occurs to me that there’s another argument for the revolving door that you rarely hear put forward: maybe we should prefer large helpings of industry input precisely in order to identify and ban harmful practices that no one actually wants to engage in, but worries they’ll have to for fear that if they don’t, the other guys will.  That dynamic seems pretty plausible to me.  You hardly ever hear about it, though, probably because it puts industry in a less than totally spotless light.  “Hey Congress, we at Foo Enterprises just thought of some really heinous shit that we could pull. It’s not that we want to do it, exactly, but please pass a law against it so BarCorp can’t do it first and undercut us.  That way we won’t be tempted.”