Honestly, I have more numbers of trades using a middleman than using a peer-to-peer I'm sure all of us here third parties will always be with us, we are so used to it, It applies in many industries it applies in Cryptocurrency.
With this can we now say that bitcoin is not performing the original privacy goal or that it is the human factor that is frustrating it because like you pointed out, third party services in bitcoin is really growing bigger apart from the exchanges, people have taken up this like the brokers and they stand in the middle to execute the transaction like the escrow service. I think the P2P service is not really getting that attention because of trust.
Bitcoin will not function and connect to the global economy without these third-party services. Remember the world was not established with Bitcoin as its main currency, Bitcoin was created in a world where there is already an existing financial system. In order to transition, Bitcoin must adjust and adapt to the existing system until it is adopted and popular enough to implement its own features without the need for these third-party processors. Aside from that, there is also authorities that hinder most of the features of Bitcoin so for now, Bitcoin has to use these exchanges since not everything in the world can be paid by Bitcoin directly.