Democracy is not a synonym for "good". Whether something is democratic or not tells you very little about whether it is worth keeping. Most things are not democratic, nor should they be.
Both corporations and charitable foundations often emulate democratic governments in some ways, most notably in their shareholder and/or board meetings. There's nothing wrong with emulating the good parts of democracy in other suitable contexts. But I'm not sure whether it's worthwhile to emulate them in every context.
Even when things are run democratically, it is sometimes better to limit participants to those who are directly involved. Would you like some democratic input from the general public as to what happens in your bedroom between consenting partners, for example?
Why is this good?
I would say the goal is to reduce problems.
> Most systemic issues we see today have a root cause in people giving up their ability to vote
Could you provide examples? Is this responsible for poverty, war, or poor education?
> preserving each person's share in the power pie
Bit of a mixed bag. Depending on your political leanings, I might give Trump and Brexit as examples of democracies making poor choices.
Why not?
Minorities need protection from majorities in democracies. And not just racial, religious or ethnic minorities. Everyone is a minority in multiple ways.
You have hobbies, beliefs, goals and connections that the majority in your country doesn't have. And they are all at risk under a democracy. This is why we don't have a "pure" democracy. This is why the Founders put many anti-democratic features in the US Constitution.
Every right you enjoy is a point where society drew a line and said "this will not be subject to a vote".
The U.S. spends about 1% of their budget on foreign aid. Yet in polls, most Americans think foreign aid should be further reduced [1].
[1] In the following poll of 1012 Americans, 81% thought foreign aid should be reduced and only 18% thought it shouldn't be: http://i2.cdn.turner.com/cnn/2011/images/01/25/rel2d.pdf