I think you’re conflating the system of government with the economic system
I am not. An economic system can also be democratic or non-democratic, same as a political system, depending on who it is primarily controlled by. Both are intertwined and influence each other. Capitalism is not a democratic economic system on its own (since "the people" definitionally do not control the economy), and it is also incompatible with a stable democratic political system.
In fact, democratic capitalism is one of the dominant political-economic arrangements in the world.
What you are describing is usually called a "liberal democracy".
In principle, democratic institutions should give the public the ability to regulate and rein in the excesses of capitalism rather than allowing economic power to become so concentrated that it begins to dominate the political system.
This is precisely what Marxists call "contradictions of liberalism".
The social tenets of liberalism preach equality before law, human rights, the rule of people, and consent of the governed. To be clear, all good concepts necessary for true democracy.
The economic tenets of liberalism (a.k.a capitalism) establish the primacy of private property, including private property over capital. (there are other tenets as well, such as a "free market" but they are not as important to this discussion)
The two are simply incompatible. Private property over the means of production definitionally gives control over economy to those who own that property. This is fundamentally antithetical to the social tenets of liberalism, and this contradiction can not be totally resolved within the framework of a liberal democracy. Even ignoring imperialism, "regulated capitalism" is an unstable equilibrium even within a closed society, a band-aid that will eventually have to be torn off one way or another; for as long as a society upholds private property as its economic model, those who control capital will be able to accumulate it exponentially, eventually being able to simply brute-force their way into politics through corruption or nepotism to remove whatever limits may be set on their power — even one slip-up can be enough to disturb the equilibrium and start the downward spiral into fascism, see the socio-political effects that Nixon had in the US.
Thus, for a society to achieve a stable political democracy, private property must be eschewed and relegated as a secondary mode of production, at least initially. Whatever that system would be, it would not be capitalism.