Florida used those electronic only machines for one of the elections a bit ago (I think after the 2000 election debacle) but moved back to the electronic/paper system after the questions were raised about accountability.
With the paper trail, not only can we verify the # votes = # voters, but we can audit the machine itself (# votes for candidate 1 = # ballots for candidate 1).
I think there was a rumor that one precinct in Texas 2008 had a machine programmed wrong so that a vote for candidate 1 was actually checking the box for candidate 2.
And our paper ballots are issued with a privacy sleeve to be used by the voter until such time as they (themselves) insert it in the machine.
As to the issue of voter ID, I agree that some forms of ID cost money (and therefore can be seen as a sort of "poll tax"). But the list of photo/signature ID is rather large and includes some forms of ID that are free (photo/signature credit card is one that pops out in my mind). But the vast majority use Driver license / ID or Passport.
Those who don't have ID are given a provisional ballot to be evaluated by a separate "canvassing board" who establish the citizen's right to vote and count that ballot if those eligibility criteria are met.
What is really interesting, however, is the vast differences between states as to how they handle the election process.... Surely there must be some "best practices" list of things that is shared among states. But since voting is left under the pervue of state gub'ment I guess it's all up to elected representatives...