The problem with this, like internet voting, is that you can be coerced.
e.g. a family member or your boss can tell you who to vote for and force you to submit that vote.
Whereas a polling both is utterly private; you are alone and free from coercion. Nobody else knows who you voted for and they have no way of telling.
In the UK, our voting is also done by paper and pencil. The votes are counted overnight by humans (with plenty of checks, independent oversight and rights of recounting) with the result typically declared the next day.
Its secure, and it just works.