Yes, and the reason you need p2p cash--or p2p anything, for that matter--is to evade government subpoenas. If you don't need that, centralized architectures are far more efficient, secure and convenient.
Bitcoin's original purpose was to create a method of transacting that could not be traced by governments, and could not be stopped by them.
The main purpose of Bitcoin is not to hide anything from governments. That turned out to be a possibility. At the same time, Bitcoin is global and for example, only a few governments are putting pressure on privacy on the Bitcoin network, and many are still not interested in it. Just as you have neutral and independent countries when it comes to fiat, so will it be for Bitcoin.
The whole thing will only move most of all services and businesses from restricted countries to crypto-friendly ones. Mixers will no longer be called mixers, they will have a new name, and their founders will do it much more carefully and with more anonymity.