When I first entered the cryptocurrency world, I was very worried about how to do the transactions. I went to various Facebook groups for transactions and messaged.
What year was this?
Except you're taking about before 2011/2012, I see no reason why one should go to a social platforms like Facebook to transact with total strangers, with the high risk of getting scammed and zero protection against it happening
P2P transactions now occur mostly over a platform, and not by the roadside directly between two people. This platform acts as an intermediary, and it being centralized or decentralized would influence the level of privacy and autonomy the user has over the funds being transacted.
About the cost of transactions being reduced in P2P, this would also depend on the mediating platform.