Publishing in a more prestigious journal usually means that your work will be read by a greater number of people. The journal that a paper is published on carries weight on the CV, and it is a relevant parameter for committees reviewing a grant applicant or when evaluating an academic job applicant.
Someone who is able to fund their own research can get away with publishing to a forum, or to some of the Arxivs without submitting to a journal. But an academic that relies on grants and benefits from collaborations is much more likely to succeed in academia if they publish in academic journals. It is not necessarily that academics want to rely on publishers, but it is often a case of either you accept and adapt to the system or you don't thrive in it.
It would be great to find an alternative that cuts the middle man altogether. It is not a simple matter to get researchers to contribute their high-quality work to a zero-prestige experimental system, nor is it be easy to establish a robust community-driven peer-review system that provides a filtering capacity similar to that of prestigious journals. I do hope some alternative system manages to get traction in the coming years.
Reputation comes from public, it requires collective action and coordination. Collective action is not easy, but it is not as hard it might seem either. For example, many open source projects in software are highly reputable without a private ownership.
That is true, but software is a much newer field overall than academia -- journals like Nature are over 100 years old, and the way prestige of journals works in academia and publishing hasn't changed significantly since the 50s. Academic publishing has a lot more momentum to change than tech, and academics have very little power to do so on an institutional level, it kinda has to come from administrators, who don't understand the problem or care.