> Why would the people who own the factories just give the output to people? What could people possibly offer, when all the things they're capable of making can be produced at zero cost?
The answer is simple, protection from them taking it by force. This is literally the reason for liberal democracies.
Dictatorship, feudalism, and other forms of authoritarian structure always come with the downside that the ones at the bottom are trying to get the ones at the top. Thus if you are at the top, you live in worry and fear of a rebelion, revolution, a coup, from your family or friends to betray you, etc.
In that scenario, your day job becomes maintaining your power and authority at all times. Which like any other job, is taxing, tiresome, and hard work. So even though on paper it seems you've got all the goods and services at zero cost, there's a tremendous cost to yourself to maintain that position when others are trying to steal it from you.
That's why, the "right to property" is fundamental. You want a society which can guarantee that right, and give you piece of mind that what you own is yours and no one is going to take it by force. So you can relax and enjoy the fruit of your labor (or inherited factories output).
One solution for this is to create a system that is governed by the rule of law, where no players is in such a bad state that they could be willing to risk it all to steal your piece of the pie. Thus a balance must be struck, where everyone can find satisfaction, even if some get to have a lot more than others.