Earlier quoted context omitted.
This is only relevant if you propose to have weekly/monthly elections. For elections every few years even a week of counting would not be a problem.
Although the longer counting takes, the more difficult it becomes for a substantial number of people to monitor the entire process. In the UK, counting takes place overnight, immediately after the polls close; it's feasible for multiple parties to ensure they have people at every location for the entire time, keeping an eye out for irregularities. If the process were extended over a week instead of a night, it become…
As things are now I see no reason of sort not to use paper ballots as the main proof of vote. Especially for big nation wide elections.