No, you’re trying to define it too narrowly. The term censorship has never referred solely to prior restraint, for the simple reason that it’s hard to know in advance what someone will do. What makes it effective is the idea of consequences: if you’re thinking about saying “military fighting machine male” in China, you know that you’re not cleverly evading the government but rather setting yourself up for retribution.
For a financial system, this is even more true because nobody sets a flag on their transaction to say it’s criminal and so any government knows that they have to retroactively pursue activity after identifying it as forbidden.
For all forms of censorship, that idea of retroactive consequences is extremely useful because it encourages people not to do things they might otherwise consider because they don’t want to leave a permanent record, and that favors those in power. For example, say someone was thinking about donating to a women’s health clinic but is worried about leaving an indelible Bitcoin record just in case that later is deemed criminal – the other side has harmed their political opposition without even having to do a thing.
Once you understand that, the connection to the exchanges is easier to grasp: that’s where they can deanonymize people and institute transaction blocks without having to go after the entire network. Since statistically nobody pays their bills in Bitcoin, this is quite effective because anyone who needs to participate in the real economy has to go through one of few companies with legal presence, and those companies can be compelled to identify their customers and block transactions involving specific IDs.
Bitcoin is a great design for censors: imagine if the Stasi could’ve blocked every transaction someone made even without knowing their identity! Send or receive a political donation and _poof_ you can’t buy food or pay rent.
