But how do you know that the centralized server does not override all records to tamper the evidence? Append-only log is useless if the actor choose to override

But how do you know that the centralized server does not override all records to tamper the evidence? Append-only log is useless if the actor choose to override all logs. So you need a neutral third party to keep the records in case the centralized server does the malicious behaviour. This can be done, I admit. But in a corrupt society, it is hard to find a neutral and trusted party. Other way is using blockchain to record the logs and incentivize the miners to maintain the nodes. You can not bribe the cryptography.