BTW, the source code we're talking about could easily be enormous, especially if you want the machines' firmware to be open too. Reviewing that source code would be a huge task. And you still have the problem of being unable to validate that the actual object code run in production corresponds to the source code you reviewed. And the public won't believe any of it anyway.
However, the Estonian governement has made a different choice and I salute that they are at least trying to do everything by the book and in the right way. Publishing the source code is a part of that. Estonia is a high-trust society (which is an incredible achievement in itself, considering they were a province of the Soviet Union only forty years ago) and they have the most functional e-identity system in the World. Voting is just a part of it. It does make many things easier and also helps economy if you can trust - and verify - your fellow man.