I think you've stumbled across a bigger issue - democracy is fundamentally broken since no one has any incentive to vote correctly.
I know a lady who's a likely Trump voter. But she also donated money to Hillary in order to get the "woman card". https://shop.hillaryclinton.com/products/the-woman-card She's pretty honest that it's just entertainment for her - like voting on American Idol.
Think about how many elections have been swayed due to "I support Obama because I'm not racist", "Bush looks like a cool guy to get a beer with", "boo yeah Trump - take that liberals who look down on me", etc? (Amusingly, neither Bush nor Trump will ever get a beer with you, teetotalers both.)
People get away with this because their vote doesn't matter. If they vote wrong, they won't lose anything. So why not just do what makes you feel good? You've got no skin in the game.
Maybe representative democracy is broken (there are reams of good texts written about it).
OTOH direct democracy may be not as broken, since the effects of voting are much more immediate and local. See Switzerland that constantly keeps voting against populist measures like lowering the retirement age. It lasted ~850 years so far, longer than almost all European states and 100% of American states.
Switzerland is compact, but even then it's a pretty loose union, a confederation with important laws significantly varying between its many cantons. This system is more or less imaginable in the US with a more restricted federal government (despite the size that was the rationale for the current multi-step representation system), and hardly even imaginable in highly centralized states like France.
People have generally not established direct democracies throughout history for a reason. I personally never want to see a direct democracy in the US, because if you want to have your faith in your countrymen destroyed go spend an hour sitting on a bench outside a Walmart and just watch humanity at work.
The vast majority of people are borderline illiterate emotional animals. You don't see or interact with them because they exist in their isolated silos of service work and personally proffered bars and TV stations, but the number of rational informed actors in any given election is in a steep minority.
I don't know the Swiss well, but I'd hope they have a much better culture to support direct democracy than what the US has, because the US would be a disaster. Islam would be banned, Hispanics would be kill on sight, police would be given heavy artillery to demolish drug dens. Whenever any international news of any kind phases the country there would be immediate over-reactionary laws passed to diminish liberty and perpetuate a culture of fear, because that is a large part of what we have now, and giving that animal brain legitimacy on the national stage would be a global catastrophe.
This may be true in some cases; this is why I think universal vote, without any limitations, is not a good idea. Voting is a privilege and a job of running (a small piece of) your country. Compare it to a jury duty.
This, again, may be false in some cases. Unless the voting process is framed as a sports match (like it usually sadly is), the emotions are much easier to keep in check, and reason is easier to listen to, even without an advanced university degree.
OTOH if you don't trust your countrymen, I wish you all the luck in importing infallible Martians to help you rule your country as e.g. a king. On this planet the only way used to be growing and educating some portion of your countrymen to be able to run the country (without running it into the ground). This applies to kings and dictators to a very high degree. This as well may apply to a wider mass of voters.
I suspect this is what happened to the Swiss: centuries of local self-rule and rather immediate consequences of it, combined with living in rather harsh conditions most of its history, must have educated people not to take the voting lightly. I don't see modern Swiss killing Muslims or Hispanics on sight (it's not the Reformation wars time), but I do see a ban to build minarets [1]. Apparently the fallout was pretty small, without a "culture of fear", Muslims fleeing the country or something like that. Sometimes a minority has to listen to the majority; it's best when the compromise is as small as this ban. Regular not listening to the majority and alienating them makes for what you fear: the mob running over the castle of the highly-cultured but insolent lord.
The point of voting is usually to determine what is right or wrong. If you're a god having all the answers, you need devotees that just obey your scripture, not citizens with a privilege to vote.
I just finished reading Kant's perpetual peace. He says something like "war protects from despotism".
I'm a Finn. During the cold war we we're situated right next to Leningrad, but still pretty much free-trade capitalist liberal democracy. Our country has very little corruption, very good primary education, free health care, conscription and long line of very very well liked past presidents. Everybody had skin in the game.
Suppose you vote wrong for some national socialist who will destroy the economy and kill the muslims. How much will you, personally, lose? I.e., multiply your actual losses by the probability of your vote affecting the outcome.
Now compare that number to the 1 Euro worth of tribal satisfaction/self righteousness/other positive feels you get from voting for that national socialist.
In contrast, consider a true "wisdom of crowds" situation. When I hold irrational views about share prices, the stock market immediately takes my money and gives it to people with rational views. Bad decisions result in immediate losses in direct proportion to how bad the decisions are.
You need some goal to correctly target that "wisdom of crowds". So first we need democracy to set the goal: Gini-index vs. Pareto efficiency. Freedom vs. security. Protection of personal rights vs. right of group self determination.
Then throw into the equation some very polarizing stuff like abortion, drugs, animal welfare, inheritance tax, immigration and whatnot. Then watch as some political entity loots government budget while people are arguing. This happens in Finland too now that Russia is weak.
democracy is fundamentally broken since no one has any incentive to vote correctly.
Correction: democracy is fundamentally broken when no one has any incentive to vote correctly.
Your argument against democracy is based on one single implementation, and a pretty flawed one at that. Maybe take a look at how other countries implement proportional representation, or where the political landscape is diverse enough that no single party usually gets a majority on its own (e.g. most of northern Europe).
I know a lady who's a likely Trump voter. But she also donated money to Hillary in order to get the "woman card". https://shop.hillaryclinton.com/products/the-woman-card She's pretty honest that it's just entertainment for her - like voting on American Idol.
Think about how many elections have been swayed due to "I support Obama because I'm not racist", "Bush looks like a cool guy to get a beer with", "boo yeah Trump - take that liberals who look down on me", etc? (Amusingly, neither Bush nor Trump will ever get a beer with you, teetotalers both.)
People get away with this because their vote doesn't matter. If they vote wrong, they won't lose anything. So why not just do what makes you feel good? You've got no skin in the game.