It's the best solution because attempts on it don't scale; any attempt at it requires either everyone in the room be in on the fraud (and it takes just one person to break that) and even then, going through ballots by hand takes a long time, where the crime can be found at any point due to physically being there.
E-voting? One hacker can reprogram thousands of machines, possibly not having to even be in the country, anonymously. It gets even worse when you have online voting, because then you have a whole host of potential exploits, like MITM, DDOSing targets like libraries, gathering IDs, etc. When you consider the amount of money running on elections, it's not unthinkable to consider there could be state-sponsored hackers, so there's no problem of resources there. And this is all assuming the hardware and software aren't already compromised by the manufacturers; considering we've seen compromised hardware coming from China it's a very likely possibility.
E-voting? One hacker can reprogram thousands of machines, possibly not having to even be in the country, anonymously. It gets even worse when you have online voting, because then you have a whole host of potential exploits, like MITM, DDOSing targets like libraries, gathering IDs, etc. When you consider the amount of money running on elections, it's not unthinkable to consider there could be state-sponsored hackers, so there's no problem of resources there. And this is all assuming the hardware and software aren't already compromised by the manufacturers; considering we've seen compromised hardware coming from China it's a very likely possibility.