I think American voters should grow spines, and at least ALLOW their votes to be linked to their names. This way, you could verify that your vote was recorded correctly. I think most Americans, after pondering the options, would elect to link their names to their votes.
It would also make it easier for citizens to view the voter roles, and identify cases of dead people voting, or more people voting than actually showed up in a given precinct.
The leadership of both major parties, you can be assured, would fight this simple and logical proposal tooth and nail.