The earliest well-documented democracy is that of Classical Athens, and all of our literary sources on Classical Athens were written by wealthy men. Unsurprisingly, they all claim that what you're asking is exactly what happened. One of our earliest and best sources is the pamphlet written in the 420s BC by the unknown author known as the Old Oligarch, who puts it like this:

They know that it is the rich that pay for the choruses, while the common people are paid to be in the choruses; the rich pay for athletics and for triremes, while the common people are paid to row in triremes and take part in athletics. The common people think that they deserve to take money for singing and running and dancing and sailing in the ships, so that they get more and the rich become poorer.

-- Old Oligarch, Constitution of the Athenians 1.13

While tendentious, this description of the system of Athenian democracy is hardly exaggerated. The rich paid for all public offices and services, while the poor received pay for carrying out their civic tasks such as jury duty and military service. The rich paid all the tax; the poor paid no taxes at all. The democracy had no qualms about reducing their wealthy citizens to poverty with expensive liturgies (individual shares of public expenses, like manning ships), threatening them with exile and loss of citizen rights if they failed to pay. We know of several cases in the 4th century BC in which wealthy men were forced to borrow great sums of money or to bankrupt themselves to meet their obligations to the state. In wartime, if the state was short on cash, they would come round for "contributions" (eisphora), and only those above a certain property level were liable to pay. The common people watched the behaviour of their wealthy citizens closely, and if there was any hint of misbehaviour, it was before a jury of commoners that the culprit would be judged. Mercy was not to be expected.

This is a large part of the reason why, unlike modern political thinkers, some of democracy's wealthy critics in the Classical period did not regard "people power" as a system of equality of all citizens. Instead, they regarded it as a form of class government: the rule of the poor over the rich. To their minds there was little difference in practice between democracy and oligarchy; in both systems, one class ruled at the expense of another. The group in charge would do what it could to keep the subjected group down and take what it wanted from them. The greatest enemies of democracy went further than this, and claimed that radical democracy was functionally identical to tyranny:

A democracy of this nature is comparable to the tyrannical form of monarchy, because their spirit is the same, and both exercise despotic control over the better classes, and the decrees voted by the assembly are like the commands issued in a tyranny.

-- Aristotle, Politics 1292a

It was impossible for these authors to discuss the issue without letting their own position shine through: the rich are indicated with the euphemism "the better classes", and readers are to take it for granted that these would never be as despotic and lawless, even if they were given absolute power. There is an interesting philosophical exchange on this topic in Xenophon's work, in which Alkibiades half-seriously argues with Perikles that ultimately all forms of government are tyrannical, but democracy especially so:

Perikles: Everything, I think, that men constrain others to do “without persuasion,” whether by enactment or not, is not law, but force.

Alkibiades: It follows then, that whatever the assembled majority, through using its power over the owners of property, enacts without persuasion is not law, but force?

-- Xenophon, Memorabilia 1.2.45

In the dialogue, Perikles has no answer to Alkibiades' cleverness, and instead scolds him for trying to be clever for its own sake, rather than making a constructive argument. But the dialogue stresses a fundamental problem with this view of democracy, and with all political systems theory as conceived by the Greeks: if even democracy, in practice, meant the rule of one group over others, was there any way to avoid oppression? Or would all societies simply have to choose between having the few ruled by the many, or the many by the few? Aristotle puts this somewhat cynically at the beginning of his survey of existing forms of government:

Tyranny is monarchy ruling in the interest of the monarch, oligarchy is government in the interest of the rich, democracy is government in the interest of the poor, and none of these governs with regard to the profit of the community.

-- Aristotle, Politics 1279b

Given this winner-takes-all situation, how could any form of government be considered more just and desirable than another? How could the oppressed faction really object to their oppression, when they knew they would do the same if they were on top? Again, Aristotle clearly struggled with this question, and poses it directly to his audience (1281a):

If the poor take advantage of their greater numbers to divide up the property of the rich, is not this unjust? (...) But is it just that the minority and the rich should rule? Suppose therefore they also act in the same way and plunder and take away the property of the multitude, is this just?

Thinkers like Plato and Aristotle constructed ideal constitutions that were intended as superior blends of the better features of monarchy, oligarchy and democracy. But they knew such things did not exist in practice, and sometimes even critiqued each other's ideals, arguing that such things could not exist in practice. The reality was simply that every form of government led to the oppression of some. Tyranny was evil, because it led to the oppression of all; but the socio-economic elite could not argue that it was better for the uneducated masses to rule than for them, the educated rich, the ones they called "the best" and "the beautiful and good", to take the reins. The most realistic commentators, then, offered no alternatives, and simply recognised that democracy was in the best interest of the largest number of people. They understood, too, that the masses would bitterly defend their achievements against encroachment by the rich, who would set out to deprive them of all the rights they had gained. These elite authors saw, ultimately, that this meant their own kind must suffer:

[The common people] recognise that the ruler is necessarily hated by the ruled, and that if the rich and good men in the cities become powerful, the rule of the common people of Athens will not last long. This is why they deprive the good men of their citizen rights, take away their money, drive them into exile, and execute them, while increasing the power of the bad.

-- Old Oligarch, Ath. Pol. 1.14

Indeed, this source, perhaps more than any other from the time, acknowledges that even if democracy is bad for the rich, the alternative would be much worse for the poor:

Everywhere on Earth, the rich are opposed to democracy. (...)

If you are looking for good laws, the first thing you will see is that the cleverest men make laws in their own interest. Second, the good will punish the bad and the good will take counsel about the city and will not allow madmen to become members of the Council, nor to make speeches, nor to attend the Assembly. As a result of these excellent decisions, the common people would soon plunge into slavery.

-- Old Oligarch, Ath. Pol. 1.5, 1.9

The final point is exactly as emphatic as the translation suggests. The word really is slavery (douleia); the result of allowing the oligarchs to rule would be that the poor would be stripped of their rights and their freedom, and be reduced to the property of the rich. This is what this oligarch himself admits; this is what he recognises that the Athenian democrats know. They rule, then, not out of greed, but in self-defence. They will have either democracy or slavery; they can either take from the rich, or be taken by the rich. In the final instance, this author knew the score, and suffered no manufactured outrage (2.20):

I can forgive the common people their democracy; for anyone can be forgiven for looking after their own interests.

It would be easy to see this attitude as a sort of grudging benevolence, or a recognition of defeat. But in reality, we should also recognise it as a point against over-dramatic interpretations of Athenian democracy as a regime that deliberately plucked the rich like chickens. If the rich were able to live with it, even if they did not agree, can it really have been that rapacious and kleptocratic?

In reality, it would be more true to say that the Athenian democracy managed a relationship of mutual dependence with its rich citizens. Much as it feared and despised oligarchs, it needed their money to function. It also needed the educated classes to provide military leadership and entertainment. It subjected them to heavy obligations, to be sure - but there were substantial rewards. Democracy allowed shiny career paths to ambitions members of the leisure class; it regularly voted special honours to its benefactors, and paved the way for rich men to towering social status and an everlasting reputation. This was a system even staunch oligarchs could work with, and therefore one they were mostly willing to pay into, even if the cost was at times crippling.