This is false. I know this is a common thought on HN because some formerly popular youtuber did a video about this topic that is still regularly reposted here, but he was already wrong in theory back then and it is certainly wrong in practice today. Secrecy/anonymity and verifiability are no longer mutually exclusive as anyone who is well versed in modern cryptography will be able to tell you.
Also, you still have to convince the public.
There have also been earlier implementations like this one: https://github.com/benadida/helios (corresponding paper https://www.usenix.org/legacy/event/sec08/tech/full_papers/a...), although it still lacked coercion resistance. But it already uses zero knowledge proofs, which is at the core of anonymous yet verifiable systems.
Public doesn't need to know the details. Production of paper, printers is quite complex and so production of the pen. Yet people are not concerned about that when voting and we don't publish schematics of a printer that printed the ballots.
Except that people know what paper looks and feels like, they know how it absorbs ink, they know its various properties, they can _read_ whatever is printed on them, and they can see that the marks they make (or a ballot marking device does for them) are faithfully visible on the paper. With paperless machines there is nothing comparable.