Power is not a mental need nor a physical one, it's a tool. Capitalism selects for those that can best get the most profits, ergo power is useful in achieving those ends. It isn't about making "good" decisions, but profitable ones.

Why do people want to rise in hierarchies? Not for money alone.

This is a cop-out answer. People don't have a natural desire to "rise in hierarchies." If that's the best way to improve your material conditions then people will desire to rise, not for an obsession over power or domination.

How to settle among different classes of workers?

If you mean between the peasantry and proletariat, the answer is to industrialize agriculture and fold everyone into the proletariat gradually (alongside collectivizing production and distribution to erase class). If you mean between, say, plumbers and engineers, those are the same class.

Only without UBI. If workers can walk away, they can ask for the value of their work and capitalists could only get the value of their own work.

Utter fantasy. UBI is just a form of social welfare, but with capitalists in charge of the state UBI will only exist in a manner that benefits capitalists. The state isn't above class struggle, but within it. Further, capitalists do not labor. The day to day management of companies is done by workers, capitalists contribute nothing but the fact that they legally own the tools.

No, capitalism is all about preventing competition. It’s liberal markets that need competition. With competition there are no profits above production costs. The profit of capitalists does not only come from underpaying workers but also from overpaying buyers.

Profit comes from underpaying workers. Profit is made by selling commodities for their value, which is made up of raw materials, tool usage, etc called "constant capital," and for wages, called "variable capital." Constant capital is crystallized prior labor, the profit comes from paying a worker for only a small portion of their labor time, regulated around cost of reproduction of labor (ie, minimum customary living standards). Monopoly prices raise the rate of profit, which is why companies try to seek monopoly, but they also need competition in order to keep circulation of commodities flowing for their own valorization of invested capital.

Capitalism kills itself, it's a contradictory system.

Commodities would still be bought by workers if there is only one capitalist. Earth would be one big mining town.

Think of it this way: If a single capitalist owned everything, then cost of goods collapses. There is no circulation anymore, only planned production and distribution, and absolutely no organized class for protecting said single capitalist. Capitalism would cease to function. Company towns only "worked" because they existed in the context of a grander market that the capitalists could get all that they wanted from.

If somebody owns everything they can command everything. Why would they need profits?

Because that is the driving basis for capitalism and material gain under it. That's why I'm saying that this hypothetical is impossible and would collapse immediately, just like anarcho-capitalism. It fundamentally misunderstands how capitalism works.

No. The left seems to look at workers and sees lack of organization. But the workers don’t see workers, they see apprentices, skilled workers, bosses, management. They see women and men, they see nations and races. There is no joined identity. There is hardly anybody who wants to be organized as a worker.

This is a very western viewpoint, and one that is increasingly incorrect. As capitalism decays, class awareness is rising alongside class struggle.