Universal Comprehensibility
Pencil and paper has one advantage that no electronic or mechanical system can claim: it's universally comprehensible.
90% of the population can't program a VCR, let alone a computer. The Source Code for the voting machines isn't a lot of use to them. They just have to take someone else's word for it. Furthermore, even if you did go to the trouble of downloading the code from the Election Bureau's website and checking it line by line, how do you know that that's what the machines are actually running?
The problem with electronic voting systems -- and it is a limitation of the universe rather than a limitation of current technology, so nothing can be invented that would mitigate it -- is that what is actually counted is only a copy of what the voter did, and thus it can be changed without the voter's knowledge. Any "layer of security" you can bolt on top of that won't make any difference, because ultimately it's just a diversion which solves the wrong problem (and occasionally creates new ones; for instance, receipts still don't prove anything and can be used for nefarious purposes).
Just because you know how *your* vote was recorded, that doesn't tell you J.S. You still don't know how *everyone else* voted. The Authorities can publish absolutely bogus results and as long as they can tell *you* correctly, at some later date, how you voted, then you have to be happy with that.
Manual counting involving representatives of all candidates exploits the pre-existing adversarial relationship between them: nobody trusts anybody else, so the only way not to get called out is to tell the truth.