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.
Definitely the human factor that is mitigating against this original plan of bitcoin P2P transactions, that assures privacy between two parties. And this is as a result of mistrust, because nobody wants to be scammed, therefore it necessitates the importance and emergence of the middleman in transactions. I think that as long as there is no technology on ground yet to guard against being scammed in P2P transactions, then the exchanges and other forms of third parties will still be invited as intermediaries in bitcoin transactions. I really look forward to the day when we won't need any centralized exchanges to transact bitcoin, that was made to be decentralized.