The question then is, why do people choose the way they do, both when buying and when running a company? To me it seems, they don't because of some external pressure (like monarchy requires).

The ideas that people have are shaped by their Material Conditions, and people generally act in their best interests. People will buy what is available in the market, and Capitalists work to accumulate more and more money in an M-C-M' circuit.

The point can be summed up as a question: Why don't people run (more) non-capitalist services and productions, and why don't they prefer them when looking to satisfy their demand?

These are 2 questions.

1. People generally don't run Socialist services as frequently because in the framework of Capitalism, it is excessively difficult to gain the Capital necessary to start one, and furthermore the people with access to Capital continue to act in their own interests and accumulate more profit off of ownership.

2. People do not care where their commodities come from, largely, as they work for their income and thus their access is limited by the money they have.

These non-capitalist things exist, it's certainly possible. But as far as I know, they are all very niche. Like a communal kitchen, some solidary agriculture or housing project. Heck, entire villages of this kind exist.

This is known as Mutual Aid, which is a big cornerstone of Anarchism. The issue is that Anarchism generally relies on individuals making the right decisions due to their horizontal structures and has issues with scaling horizontally. These structures tend to have great success locally, such as Food Not Bombs feeding people, but without strong organization scaling becomes difficult and action becomes unfocused.

So the alternative is there, but it requires actual commitment and work. I don't see how capitalism could be abolished in an armed uprising (in contrast to monarchy). But it can be replaced by alternative projects. Partially. Why are they so small and few?

Why don't you think Capitalism could be abolished via revolution? It's been done before.

Secondly, it is not simply capable of being replaced entirely via parallel systems because that depends on individuals outcompeting the immense resources of the Bourgeoisie. It's certainly possible at a local level, but at a state level takes enourmous power and unity.