This is partially correct, China is not a monolithic entity that fully marches in lockstep with Beijing.
But the solution to the problem of uncooperative governors is the application of soft power (media, agitprop, appointments, rewards, threats, denunciations and disappearances, liquidation of problem people, their families, their friends, their pets, etc), not some over-engineered technological non-solution that still relies on the cooperation of all the parties in question to work.
A blockchain can't enforce that anyone actually enters data into it, or that the data that is entered isn't garbage. A snail-mail package containing data sent to Beijing has the exact same immutability property for the only party that cares about it - the national government.
Something like a blockchain is useful when peers don't trust eachother, but all care to build a shared consensus. When the peers don't care about consensus, and a central authority with the power of pit and gallows exists, none of those usecases hold.