With anonymous voting, resistance can grow over time. Election #1 may see 1% of voters vote against the despot. Encouraged by that, the people increases that to

With anonymous voting, resistance can grow over time. Election #1 may see 1% of voters vote against the despot. Encouraged by that, the people increases that to 10% in election #2. Further encouragement sees that go to 60% in election #3. With non-anonymous voting, the people would still be encouraged by that 1%, but also seeing 1% of voters lose their job/get beaten/go to jail/… puts a serious damper on that encouragement leading to “I’ll vote against next time”. That’s why non-anonymous voting doesn’t work against despots.