For a counter example: if everyone decides for themselves what they want to do with themselves, that's not democratic at all. Doesn't involve any voting etc. But it's systematically distributed power.

And that kind of arrangement is common for most aspects of life in most places.

Eg you can decide for yourself what you want for breakfast or whether you want any breakfast at all. Throughout most of history you could also decide for yourself what kind of substances you want to put into your body.

Though in the last hundred-and-something years there has been a lot of democratic (or autocratic..) control over that in many places. Cannabis and alcohol make for interesting example of how (democratic or not) government control waxes and vanes.

In most countries, where you go for a holiday is up to you. But eg Americans' democratically decided that they can't go to Cuba without a special license. (By the way, I would call this the opposite of distributing power. They centralised the decision.) In the bad old days, people living in the German Democratic Republic famously were really restricted in their holiday-abroad choices. (But whether one wants to call their regime 'democratic' is rather debatable.)

But the right solution to East Germany's travel restriction wasn't to put every citizens travel plans under democratic control (eg up to a vote by all the citizens). The Right Thing to do was to just lift travel restrictions, and that's what they did when they joined the Federal Republic of Germany.