It was an intentional propaganda strategy to separate references to the government of an official enemy country from references to that country (see also "the Houthis" and "the Taliban"), and it also looks like "СССР."

The reason why ordinary people parrot it is because that's what it was designed for. The proper term for "CCP" is "China." Referring to the Chinese government as the "CCP" (or the CPC) is like referring to the US government as the "Demoplicans" (or the Democrats and Republicans.)

Instead, we just say "the US government" or "the US administration."