There's a good reason we should not have tests. A democratic system as we now understand it broadly means that every citizen is enfranchised. As soon as you start implementing tests, you being to interfere with the right of an individual to vote on arbitrary grounds.
While you could try to use this argument to argue for children's suffrage, I'm not sure it holds. Tests like the above have no cutoff, they can apply to someone their entire life. There are many things we don't allow children to do, but once they come of age they are (largely) free to do so. I don't know why I'm arguing against an argument I just came up with that might, hypothetically, be used as a counterargument to my original argument, but that's the internet for you.
Yes, that was my point: any kind of test of this nature is incompatible with democracy as we now understand it. But that also means that democracy as we now understand it has a serious flaw: people can vote regardless of how well informed they are or how good their judgment is. That fact, combined with the fact that one person's individual vote only has a very small impact, means that it is rational for voters not to bother being informed, but to vote on very superficial factors. As a result, in the US, we have a Congress with approval ratings in the single digits but reelection rates for incumbents in the high 90s.
I'm normally the first person to say that we should stop all the ill-informed people voting (which tends to mean excluding the majority of the right-wing), but this is so subjective that I don't even know if it's a real dilemma.
Ultimately any compromise will frustrate people, it's where we draw the line that counts.
Apropos of the system in the US, I think your politicians are far more partisan than those in Europe, although we have our own fair share of stupid policies based on popularism and ill-thought-through ideology.
But that kind of agency is very, very weak; my vote has only a miniscule impact on who legislates. I personally would be quite willing to trade that tiny bit of agency for the government's agreement to not mess with so many things.
> Apropos of the system in the US, I think your politicians are far more partisan than those in Europe
I think this is true, and there are two reasons for it that I can see, one good and one bad.
The good reason is that there is more diversity of thought in the US in general, and that gets reflected in a wider range of political viewpoints. Some partisanship is based on honest differences of opinion in areas where nobody really knows the right answer; in such cases, it's better to have multiple viewpoints represented and give each of them a chance to try things out.
The bad reason is that more Americans have crazy beliefs, so that we have people in, say, the US Congress with widely different beliefs even about matters of simple fact like how old the Earth is. Of course that's going to make it harder to govern and increase the likelihood of highly polarized debates with no resolution.
As much as I would love to see these things done, there is no way to do them in a democracy, because how would you determine the content of the tests? In a democracy, you would have to vote on them, which just brings you back to the same problem.