The original internet was funded by taxes. Since then, you are right. When a private company invests in it’s own infrastructure, it has a right to make its own terms. But the internet is global, so every private company has to interface with other infrastructure at some point.
The “original” Internet was a series of private links, provided by telecom providers that connected multiple institutions, mostly colleges together. When the operations and maintenance of these links became burdensome to these institutions, the job was “off loaded” to private companies called internet service providers. That is part of the strength and resiliency of the internet.
No one person owns or even CAN own, the internet. It’s original purpose (long exceeded) was a DARPA project to provide a resilient communications infrastructure in the event of a nuclear war. When the shift happened to the ISP model, the internet became far more of a co-op than a utility.