Honestly, I think the issue here is more your lack of education/awareness than anything else.
Like electing citizens to office at random
Ancient Athens had a system to do exactly this for a period of time.
Or even a pure democracy in a modern sense
Check out the Democratic Confederalist system currently in practice in the Autonomous Administration of North and East Syria (commonly called Rojava). It's not strictly pure democracy, but that's a core principle, and it's MUCH more participatory than virtually any other governmental system on the planet.
The big issue here is that education is always political, even if you don't think it is. I'm guessing, based on your writing here, that you were educated in a western liberal democracy. The curriculum you were taught in school, especially with regards to governmental systems, civics, and history, is heavily influenced by the ideology of your country: liberal western representative democracy. I had the same education in school growing up. The curriculum is only interested in presenting alternative forms of government as a way to show how great the one you were living under is. "Monarchy was bad for these reasons, so we replaced it with liberal representative democracy." "Fascism is bad for these reasons (while ignoring all the ways it's very similar to our current system), so be happy you have a liberal democracy." "State communism was authoritarian and bad, so be happy you have what you do." Etc.
They never talk about the shortcomings of their own system, or the benefits of others, because they aren't trying to educate a bunch of radicals who might one day overthrow the system.
There are a lot of people thinking of alternative forms of government. For my own personal ideological biases, I'd recommend reading stuff by people like Mikhail Bakunin (1814-1876), Peter Kropotkin (1842-1921), Murray Bookchin (1921-2006), David Graeber (1961-2020), or Abdullah Öcalan (1948-).