I invented something like this myself that used a checksum based form of ensuring data can't be tampered with. The key point is that anyone can look up how it recorded THEIR vote without anyone else being able to. Uses a hash of social security number for that (plus other personal identifiers). Websites can be written to allow a simple form-based trivially simple gui that allows anyone to look up how their vote was r…
Part of the reason is that to compromise a paper ballot you need thousands of corrupt volunteers (and if you can find them, you have much bigger problems anyway).
The other part of the argument is that the security isn't enough for a voting system. You need /obvious/ security, and a mathematical proof just isn't obvious enough.
Also: ethereum. And your system probably suffers from allowing people to prove who they voted for.