The important properties here are immutability, transparency and authentication. This could be done by a centralized server. For instance by keeping an append-only log with signed voting records which is regularly published, where each entry contains previous entry ID. Like git...

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.