Voting is an incredibly hard problem. For instance, your description "anonymous but prevents double voting" is ripe for fraud: I go around paying people to vote

Voting is an incredibly hard problem. For instance, your description "anonymous but prevents double voting" is ripe for fraud: I go around paying people to vote for me (or intimidating them into doing so). The secret ballot, cast in public, is resistant to that attack. More generally, one requirement of a voting system is that people trust it. Any elaborate system, no matter what it's theoretical advantages, can have a hard time meeting this hurdle because there are many people in the population who are NOT experts on cryptography and won't be comfortable with any elaborate system.