That may already be happening https://openwebsearch.eu/
The role of a government in a capatilistic society is to basically do the stuff that isn't profitable for corporations to do without exploiting the population. For example build roads, because if a corporation did that there would be tolls everywhere and it would be hard for poor people to improve their living standards if they couldn't economically move around. That seems to have happened on the internet. The internet is in the commons and everyone expects it to be free, the problem is that the infrastructure to navigate it was built by corporations and now we have to pay tolls through ads and trackers