Republics might have worked... in a time that isn't the globalized and politically polarized world of today. Democracies work when you have a unified group of people with a coherent perspective, otherwise it's just people voting against ingroups and outgroups. Representative democracies/republics inherits the same flaws and manages to introduce new ones, such as the elected representatives being motivated by short term gain rather than the long term health of the country.
"Democracy" is a buzzword politicians frequently try to appeal to, as if it is good in of itself. People are indoctrinated by schools to think that voting is good. Processes are not things that are "good" in of themselves. They are conditionally good, so long as they produce the desired results.
In reality democracies are illusory. The real power remains in the hand of the super elite who make the actual decisions. As you can see with the 2020 election, we do not live in a democracy, and if we do then it's bad. We lack to ability to accurately count votes and the system does not address this. Even if we do pretend that Biden was legitimately elected, then that would mean that the majority of Americans are insane and we should do away with elections, as they voted to elect a ruler who clearly suffers from Alzheimer's and has a long history of corruption. The majority of Americans voted to be ruled by someone who is incapable of holding office morally and mentally. Things are not justified by elections.
The US is not the only accessor of democracy’s failings – just take a look at Venezuela, an oil-rich country that is on the brink of starvation due to the “election” of socialists. Clearly, looking at the outcome of their country, the system must be replaced with something that functions better.
At least in a monarchy, there is less bullshit. It's unambiguous who the true decision makers are, and how the responsibility for a screwup lies with. A ruler for life/hereditary ruler's self interest is the longterm wellbeing of his country (as opposed to elected politicians who will sell their country's future for immediate gain), and with their life on the line they are highly incentivized to do well.