Liberal democracy works fine in that it makes people less miserable than the alternatives, but there are many other sources of misery from which it can't protect a society. It takes more than a system of government for things in a society to 'work'.

I don't believe there is enough historical evidence to make such a bold claim, it could just be a phase for all we know.

The claim is that it makes a person happier to have a say in who governs their society, and the freedom to believe and express what they want, as long as it doesn't hurt their neighbor.

That is not a bold take.

A feature of democracy is that a majority can set the course of their society by voting.

A feature of liberalism is that a minority can attempt to become a majority by argument.

If there were a nefarious foreign power pulling the strings of my Western-style democracy (which, where I live, would be an unhinged belief), I'd use my vote and my voice to oppose it, not jettison the vote nor jettison my rights.