... which is a completely different problem than funding services such as those provided by facebook and the benefits in terms of communication possibilities those services provide.
One problem is the funding of infrastructure, another problem is the funding of the production of "content". Those happen to be intertwined a lot at the moment, but that's not a technical necessity, but rather a result of the current business models that build on surveillance (and the creation of de-facto monopolies and the subsequent potential for vendor lock-in).
It would be relatively unproblematic to fund development of infrastructure with donations or even tax money--think development of open standards/protocols and possibly reference implementations of those protocols. Then, it's unproblematic for most people to pay directly for the operational costs of processing and storing their own data (that is, computers running implementations of those protocols, storage devices, bandwidth). None of that requires anyone to have any access to or control over the actual content that people communicate. For that aspect, there is no need to have "websites". The central entity is completely unnecessary, you simply pay directly for the actual costs of the technology without the need to reveal anything about what you communicate or process or store.
As for the funding of content production: I think we have to have some possibility to pay for that anonymously if we want to keep democracy stable. We can buy newspapers with cash without leaving much of a trace in anyone's database as to which paragraphs of which articles we read. Letting terrorism paranoia destroy that would be a terrible idea. Also, as I have repeatedly said, I don't understand why you seem to be constantly equating advertisement and surveillance. Just because you can use surveillance to make advertisement more efficient, doesn't mean that advertisement without surveillance is useless.