I can't speak for NACHA (the governing body that came up with ACH), but I believe the goal was to make it an electronic equivalent of a paper check.

If you think about it, it's pretty easy for someone to create a fake check based on someone's account/routing number (which, as you correctly say, it's not private information because is on the bottom of every check you write), put it in an ATM machine and debit someone's account without their permission. ACH is really no less secure than the current security protocol for checks.

Not that I think this is a good idea, but this might be a possible explanation of why ACH was designed this way.