Sorry, after posting my comment, I went back and elaborated a bit and just so happened to address the questions you asked in the meantime.
Putting a piece of paper in a box is something everyone understands how to do, even elderly people who have never touched a computer -- how is electronic voting easier?
> would require fewer people (i.e., election workers -- who are already in short supply)
They are? I can't believe it would be more expensive to hire a few more election workers for one day than we're paying for these machines.
> would give us results much quicker,
France uses paper ballots and results are known within hours.
> and would be easier to verify/authenticate later (in the event of disputes).
This is not realistic. We are never going to go back and change an election result whether or not records of the votes were saved. Cf. Florida 2000.
Part of the witness duties should be making sure the votes for that polling location are counted accurately and there is no way to do that with electric voting systems. It's just a black box you have to trust.