Quis custodiet ipsos custodes?
One important reason to not implement a license system that it is much more vulnerable to manipulations. Whoever runs the tests gets the power to decide who can vote and who cannot. There is no objective measure of "voting fitness" - the test's difficulty can range from only very simple questions that most people should already know without looking them up (who is the current head of government? etc.) to something that you cannot pass without at least one month of preparation. Where do you draw the line, even in an "unbiased" test?
How do you make sure that the test designers are fair? As it is, many ruling parties in democratic countries try to use their power to exclude certain minorities from voting. They cannot directly forbid it because the right to vote is universal - but they are sometimes trying really hard to set up some barriers to make it very inconvenient to vote for groups they view as leaning towards their political opponents. Or take, for example, gerrymandering. In theory, it is great to make every vote count exactly the same, but in practice, you can see what it leads to. Giving out licenses would make things much easier for parties that try to shift elections in their favor.
By the way, did I write "unbiased"? Even that is an illusion. The test will be biased by design: It is specifically targeted to exclude uneducated voters. A lack of education correlates with a lack of income. Thus, the final vote will shift towards the opinion of the rich. Is that even desirable in the first place? Elections are democracy's way to give the people a way to "correct" their government if they disagree with it - the other way to do so used to be revolutions. There are many disillusioned voters right now already. If you completely take away their right to re-join the democratic decision making process, they won't be happy, that's for sure.
At the end of the day, the only "objectively desired" outcome of an election has to be to accurately reflect the opinion of the entire electorate. If the majority of the people are making "stupid" decisions, well, that sucks, but it is their right - not only because of ethics, because of necessity. They will continue to be existant even if you chose to ignore them. So you have to listen. Many of the world's politicians make the mistake to think otherwise.
If you want to have less uneducated voters, the most sustainable way is .. to educate them.