I think that countries need to switch to an open ballot because of the conflicts between the secret ballot and hybrid direct/representative democratic systems and electronic voting (which thanks to advances in cryptography becomes more viable every day). However the only reason the US didn't have huge trouble with an open ballot was the decreased motive for vote buying, since all voters in that time were white males - and usually from the upper classes at that (during much of that period, the white males also had to own land and/or pass an "intelligence test" and travel in ways that weren't practical for the working class in order to vote). In short, the country club crowd had no reason to pay or coerce each other to vote the way they all wanted. The fledgling democracy would've been clearly identified as an oligopoly by today's standards.
An open ballot being shoehorned into today's world would cause corruption and vote fraud to skyrocket. A switch to an open ballot system, which again I think is a worthwhile pursuit, will need to be accompanied with very strong technical and legal countermeasures to prevent this.