Indeed, twin studies form the strongest leg of Bryan Caplan's argument in support of the signalling hypothesis in his book The Case Against Education, which I highly recommend anyone trying to refute it read and try to debunk. If you want an itemized list of citations this is where I'd start.
Hey, it's a free country. :) When I imagine other hypothetical books titled things like The Case Against Capitalism, The Case Against Monogamy, or The Case Against Atheism, though, I note that I don't get an "insider propaganda" vibe from any of them, even though I would probably strongly dislike what they have to say.
Dr. Caplan in fact does cover this point in TCAE, of course. He comes to conclude that only about 70-80% of the effect of education is attributable to signalling. A solid 20-30% still looks like good old fashioned human capital improvement, and it is largely concentrated around the basic primary education skills of reading and arithmetic. (He even has the spreadsheets where he calculated all this out online, and he has talked before about how sad he is nobody has ever tried to fiddle with the actual numbers.)
Probably not actual "2a+4=12, how much is a?" style basic algebra, though. In the United States, which is about lower-middle of the pack on PISA, about 1 in 3 adults would struggle with that level of algebra according to the PIIAC, to say nothing of e.g. the actual compound interest equation, even if the rough idea makes sense.
That's not "most people", but it's definitely "a plurality" of people. And yet life is pretty great!
My last point is that life in America is pretty great. You don't deny this, to your credit. But I don't see why that would link to "American democracy is threatened". If anything I would expect the opposite to be true.
"There's a threat to American democracy" seems like a strong claim to me by itself, let alone "There's a threat to American democracy partially because of its education quality." But, I'm an American myself, and I don't want to play inside baseball with how likely that actually seems to me.
Let's instead take Germany, where you yourself seem to be located. Germany has PISA scores quite close to the US's own, maybe slightly above or below depending on which recent year you look at.
If poor education leads to collapse, and if the two countries are about equal in their poor education, you should then be willing to accept, say, a 1 to 20 bet that German democracy will itself self-immolate in, say, 15 years. But, if poor education doesn't justify even a 5% risk of this happening in Germany, then I don't see why I would think it's a relevant factor in predicting the collapse of democracy in another country with a much longer uninterrupted democratic tradition.
(You could of course argue "No, comparisons based on PISA scores are misleading, actually there's robust pro-totalitarian brainwashing happening in US high schools that doesn't happen in German gymnasiums", or something, but (a) that's a much more precise claim than merely "US education is bad", (b) that seems really unlikely to me given I've never actually met or had an openly pro-fascist teacher at any level, and (c) even if it was true, the signalling hypothesis would still suggest any attempts at this just wouldn't matter very much by the time these kids are 25 or so.)
There's nothing mean-spirited about asking people to put rough numbers to their beliefs, even approximately. But I do think most people would be genuinely surprised to hear you think there's over a 5% chance Germany the Western democracy won't exist in a generation. If it does happen I need to remember to revisit a lot of things about how I myself understand the world.
I for one like books which are willing to explicitly make a controversial point; it makes for much more interesting reading, even if I remain in disagreement throughout.
