> Wouldn't a voting system that let people confirm that their vote is taken into account be trivial to implement?
How do you verify that your vote is actually "taken into account?"
You may be shown that your vote matches what you intended, but then it can be manipulated or discarded somewhere else in the process, beyond your ability to verify. It's like reading open source code without validating the operating system or physical machine it runs in - the entire environment contains the potential for hostility, and it's too complex for one person to comprehend in its entirety.
Also, any such system, assuming it works as intended, may also give interested third parties a way to spy on someone's voting habits. Historically, knowledge of a person's vote has been used by governments and employers to coerce votes and to retaliate against political opponents or supporters of unpopular causes.
Let's start with a simple example. A spreadsheet with your name and your vote. You can be sure that your vote is taken into account by the SUM function.
If this is an area of interest to you, I encourage you to take the time to review the work that's already been done in this area. The example you provide doesn't even address the concerns in your parent, much less others that have been identified by those working in the domain.
As a starting point, you can review Rivest's slides for an overview.
I can't believe we still rely on trust for this kind of thing.