[PeterisP]

In the traditional paper ballot process you can observe and verify that all the votes there are recorded correctly, you just can't tell which one of these was yours, they're indistinguishable. (The local practice is that if you mark your ballot to be distinguishable - e.g. that the observers could record that Bob voted that way - that invalidates it).

And it's not just a theoretical possibility to observe - I don't know how USA does it, but for my area the counting at each district is generally observed by multiple people, including (but not limited to) the representatives of all serious parties.

[unpwn]

You say that, but this still relies on trust of the institution. If you can't verify that your recorded vote matches what you put in, how can you trust it? All the ballots could've been switched out, or something. You are choosing to trust the institution.

Everyone has different levels of trust, and I'm sure generally the chance of some grand voting conspiracy is very low; however, for me to fully trust the system I would need to be able to verify the count myself, and verify that my own vote was recorded correctly.

Personally this feels more important than some issue around buying votes etc. That is mostly illegal, and plenty of people find ways to indirectly achieve the same effect anyway...