Competition produces its own socio-economic problem, because the drive to maximize profit will drive competing capitalists to reduce labor costs as much as is feasible, thus directly impacting the livelihood of the working class in a negative manner.
Except that that doesn't necessarily happen. In a capitalist society people can go work for someone else who will pay them what they are actually worth. So the problem isn't private ownership, the problem is monopoly.
Because class conflict does not need to be "advocated", it is a simple fact of life. Capital and labor are fundamentally at odds by virtue of the capitalist economic structure: The capitalist controls the means of production, and that control transfers to all rights to the product of such industry, whereas the working class is literally powerless to be anything but the cogwheel in capitalist production, with no rights to the fruits of their labor (because labor has no fruits), no rights to control of the means by which to produce their product (because control transfers from capital, not labor), and no rights to even control their own work (because they consigned their work to capitalist control when they agreed to a wage).
This might actually blow your mind, but... some people actually want to be workers and not owners of the means of production. They are happy being paid fairly for their work and not having to manage the complexities of business. These people don't exist in conflict with the owners of production unless the owners of production actually betray their social obligation to society. And many owners of the means of production are happy to fulfill their obligation to society and, in fact, derive great happiness from doing so.
The entire economic system works by having the majority populating sell its time to capitalists so these can then use that time to churn our product for consumption which they control and distribute at their own leisure, and for their sole benefit.
Even if class harmony was a worthy goal, you would have to address this massive power imbalance between capital and labor. Why would capitalists give up that power imbalance? Why would they forgo profits for the sake of workers? Why would they advocate for labor rights or social welfare measures that limit their own control? What interests do the workers have in their continued powerlessness in the face of capital, in foregoing all rights to control production or product?
In a healthy society, owners of production that betray their obligation to society are punished for doing so. And a society with social mobility allows anyone with the drive to succeed to acquire and manage the means of production - and that means continued, persistent ownership of the means of production is not guaranteed. So there are powerful forces at work that have to be disturbed for an unfair situations to develop. And capitalism, unlike communism has a clear method for rewarding people based on merit. People who contribute more to society earn more. People who contribute less to society earn less. Communism has to contend with the lack of a clear mechanism for rewarding merit. This is a major hurdle for communism that must be addressed in order for communism to achieve it's goal. Because if profit is not fairly distributed (distributed according to the contributions made by people to society), than society becomes corrupt. That's a big elephant.
Because beneficial change will not come from people who benefit from the current system. It will only come from people who are dissatisfied with the way things are currently working.
Except that beneficial change often does (and perhaps must) come from people who benefit from a system. They do more to benefit society because of the power of reciprocity. Philanthropy often occurs because people who benefit want other people to share in that benefit. So the statement that beneficial change only comes from the dissatisfied does not mean that change can only come from the oppressed. In fact,
the oppressed often lack the means to end their own oppression (they are actually powerless to do anything about it) and so must rely on people who aren't oppressed to make changes in the system.
Contrast that to the mentality of people who strongly believe in a divisive conflict between two groups of people:
Those Who Have vs Those Who Have-Not
When people with that strong belief gain power, they tend to operate in a manner that places themselves personally in the group of Those Who Have even if it means others get left in the group of Those Who Have-Not.
It follows from the foundational belief that if you Have something, you must be in conflict with those that Have-Not (and vice versa).
So it's very difficult for communism to effect beneficial change to society. That's why a key goal of communist revolution is to take control of the government. Because only people in a position of power have the means by which to compel society to become communist.