You are missing the point. People should be less involved in the details of political policy, and more in the general direction of the country. Why? Because the average person simply cannot properly educate themselves sufficiently to have a meaningful opinion about most policy issues. Instead of actually making decisions on the basis of knowledge, the only option is to make every aspect of policy ideological, which turns it into a ****show. My political opinions are a hell of a lot better informed than most of the people I see circle jerking on Reddit or Facebook, but that isn't saying much, and it's only because I have the self awareness to know that most of my opinions would probably look a lot different if I actually understood the issues well enough to have a meaningful position.
The biggest issue with this is that it reduces every issue to a binary between two options that are so unsophisticated that they are both unworkable, and leaves no room for compromise. Our whole approach here is wrong. The same blue collar guys who get but-hurt when management makes some out of touch policy in relationship to their specific job, also think that "DEY TOOK OUR JERBS" is a valid economic theory. Representation of the people should be sufficiently abstracted that people can talk about values and results, but leave the actual details to people who appreciate the complexity of policy.
Of course, nothing will work unless people recognize and share certain fundamental values and can work in that framework.
If it doesn't work that way in politics, why do you think it'll work that way in the workplace? Management is self-interested and myopic about everything, but they at least have some exposure to every point of view. Workers are myopic about everything they don't do and tend to have an exaggerated view of their own job's importance. Should engineering get to overrule marketing just because marketing is smaller? Or visa versa? Democracy doesn't force people to resolve their issues. It can also just let the biggest group impose their perspective on the smaller group, or cause a stale mate that prevents decisions until everything breaks.
Going back the Valve example, we do know what their management structure is like, because multiple people have described their experience there, and the employee handbook has leaked. Here's one example,
https://www.google.com/search?q=vavlve+amangment+issues&rlz=1C1CHBF_enUS796US796&oq=vavlve+amangment+issues&aqs=chrome..69i57.2745j0j1&sourceid=chrome&ie=UTF-8 If you look at employee reviews of the company, there's one trend that stands out. The company is de jure a flat structure, but in reality it isn't. Things are decided by collations and cliques that have accumulated social power, so there is still a pecking order, but it's less transparent and less accountable.