You need to display all of that information, take a user's input, store it in an auditable format. Oh, and people like "small government" so making custom hardware is completely out of the question. Using a "multipurpose" computer is the economical choice.
But there's another aspect to this: if you can swap out the hardware and keep the software the same, it makes the whole thing more transparent. A jumble of 4000-series CMOS on a breadboard could hide any number of bugs/backdoors. And, perception of trust is important, nobody wants to vote on your science fair project. Also, you'd need to produce thousands of these machines to run an election. Really easy to procure thousands of commodity multipurpose machines... but you're talking about mass-manufacturing your science fair project. Hell no.
And I forgot write-ins! You don't even have a fixed set of candidates in a given election!
These are machines that read paper ballots and compute totals. See https://news.ycombinator.com/item?id=33469882
Boiling the problem down to the integrity of the hardware and software throws out the nuance of how and why exploitation might occur (and who is doing the exploiting), which has huge implications for how you make regulations and do enforcement.
Third, though, and perhaps most significantly, "traditional" optical mark reading (OMR) systems using LED or laser sources and diodes were inflexible as to ballot layout and more problematically not very reliable across varying marks (remember the grade-school requirement for #2 pencils due to OMR scoring of exams), a particularly big issue since voters are often not experienced with OMR systems and so do not mark their ballot "correctly." To address this, almost all modern ballot tabulators use a CCD mechanism to take an image of the full ballot and then interpret it via machine vision (this is not a case of machine learning, the algorithms used are actually very simple). This yields much more reliable interpretation of ballots with fewer ballots rejected to hand-counting, but requires more complex software.
It's important to understand that most US election administrators avoid hand-counting in large part because of its inaccuracy. In many US jurisdictions hand-count ballots are counted by two individuals to improve reliability, but the error rate remains higher than machine tabulation. When it is 1AM after a day that started at 5AM and you are on the hundredth ballot you've hand-tabulated since you got off the precinct floor it becomes extremely difficult to tabulate with the virtually zero error rate that US voters expect. This is not a hypothetical scenario but one that's pretty typical of US election working conditions due to the slim budget and expectation of rapid posting of returns.
And I'm unsure how adding timestamp helps with the problem you're trying to solve, don't you just need Sum(machine vote count at location X) == voters visiting location X. (Also this hueristic is kinda leaky since how do you account for voters protesting with intentional spoilers?)
Defence in depth.
A very least now they have to bring a math nerd into the conversation, increasing the footprint of the operation.
I could imagine a whole computer being there could make the rf emissions less predictable. I can definitely think of some ways of making a simple machine like that more resistant against an attack like that. Idk if the study looked into that, I can't find the study anywhere.
Oversimplification isn't helpful.