Let's get to the core principles: The white paper
Quote 1: "A purely peer-to-peer version of electronic cash would allow online payments to be sent directly from one party to another without going through a financial institution."
This clearly states that the purpose of Bitcoin is to create electronic cash to be used in online transactions without third party intermediaries. The key to this whole first paragraph is that all transactions should be free from third party intermediaries. "the main benefits are lost if a trusted third party is still required to prevent double spending".
I agree, and I suppose I should have made my qualification more clear: I am talking about a
mainstream currency that would be meant to replace existing sovereign currencies.
Bitcoin was designed as a very
special purpose currency meant to thwart government oversight into transactions. That architecture is necessarily very complicated and cumbersome compared to a digital currency not built for that purpose, for instance.
So when you drill down into the nuances of the definitions, these are both correct in one context or another.
Quote 2: From the Introduction or 2nd paragraph: "Commerce on the Internet has come to rely almost exclusively on financial institutions serving as trusted third parties to process electronic payments." "It still suffers from the inherent weaknesses of the trust based model"
In the second paragraph the white paper is explaining why peer-to-peer, trustless transactions are preferable to the current system of trust based transactions.
Yes, preferable
to those who must keep their transactions secret from their government. That's a very special purpose, and most people don't have a need for that. Most of us are content with keeping the bulk of our wealth in a bank or other financial institution.
Quote 3: From section 10 Privacy: Privacy can be maintained "by keeping public keys anonymous".
The point here is that because all transactions are stored on a ledger that is available to anyone the way to provide some level of privacy is to use anonymous public keys. Clearly the intent was to provide private transactions.
Yes, I said as much above. But of course Bitcoin largely fails at that purpose--and keeping public keys anonymous doesn't help when you can do chain analysis and triangulate where money is being moved around. As any criminal would tell you, the problem is not making the cash or keeping the cash, you get caught when you
spend the cash.
(And this is all a moot point today since I suspect most people who really care about keeping their transactions secret from their government probably used Monera, etc.).
A Bitcoin transaction with a shared node or without self custody is not what was intended.
No argument here, and I suspect that most holders of Bitcoin today don't use it the way (and for the purpose) it was designed for. People tell me, when I ask them if they physically hold their private key for their Bitcoin investment is, "what's a private key"?