Hah good point. Espiecially in practise. Because I could imagine a systems that are provably correct in principle, but when you start to imagine on which hardware, on which OS, with which network stack etc all of this would be running, then proving the whole stack of turtles down to the processor would take the lives of multiple CS-post graduates for one such machine alone. And even they would have to conclude something among the lines of "yeah we are reasonably sure it worked as intended, but there is not enough time to explain this to anybody, so you have to trust us".

I think you have the same problem with a system where votes are counted by hand.

Nope - you can personally go and check how votes are counted, verify the final tallies yourself etc. All parties that participated in the vote send one or a few people to all voting precincts, and each of them can carry on parallel votes, make sure votes and tallies are safe on the way to bigger centers etc.

Of course, it's not possible for literally every citizen to this themselves, but since citizens already have to trust the party they are voting for to some extent (otherwise, why care about the election?), this works out very well in practice, especially if you add a few citizens organizations and international organizations in the mix monitoring as well.

Electronic voting is orders of magnitude more complex, even in simple centralized schemes. In more decentralized schemes, it becomes completely, hopelessly intractable to ensure validity unless you chose to blindly trust hardware and base software (microcode, BIOS, disk firmware etc.). And the same argument about trust above doesn't apply here, as it's not your preferred party's representatives that have created the hardware etc.

This is why electronic voting is unconstitutional in some jurisdictions - Germany, at least.