For monetary value storage we kind of do it in a public blockchain with public code, but for something INFINITELY more important than money we trust a closed group that designs in secrecy?
How come?
The introduction of digital systems and code will never increase trust and security, it will decrease it.
The code being open is irrelevant. There's no guarantee that the system as a whole is doing what the code says. And even if there was, it still adds to the complexity.
Digital systems will create 1,000 new ways to cheat and deceive and interfere.
Elections are special and I think the society needs to abstain from the temptation of 'efficiency' and 'speed' as promised by digital systems.
Entities that push for the introduction of digital systems are not interested in increasing the power of people or increasing trust and transparency.
What they like to do is to reduce the obstacles in their way and concentrate the power. They will control the supply chain and a handful of vendors that make the machines and the software and control the network.
After a while the elections will gradually move more and more towards a "the super computers said ..... won, just trust us it's all totally secure and verified by our super state of the art AI and machine learning models, are you saying you are smarter than those?!" system.
Code being open doesn't mean anything unless you can verify the code running on a machine at the time of voting (adding another layer of complexity). It's not just voting software though, the rest of the system needs to be verified too (both software and hardware).
Not sure why you compare blockchain here either, no developed countries I know of use blockchain in their monetary authority or try to obscure voting processes from the public.
The entire premise of conducting elections on networked computers is a shaky one. We do not have any of the problems that are allegedly solved by using electronic voting machines: paper-based elections are not too expensive, they're not too slow, they're not too untrustworthy. The only aspect that computers in the voting booth could conceivably solve is speed, at the expense of electoral trust and quite possibly tax dollars paid.
In as far as computers are involved in doing an election, they should only be used as adding machines and to transmit local results up to the responsible officers. Even then, thorough checks on the machines—hardware and software alike—have to be conducted, backups such as telephones and fax machines should be thought of, and, most importantly apart from having an eye on the procurement of the required manpower, a consistent paper trail has to be collected and kept safely sealed for the case of re-counting, of which at least a single one should always be done.
It has become sort of a mantra for some tech-oriented people and society that automation is good, computers don't err, and less people on the job is a good thing. None of these is a given. Quite the contrary, take in lots of paid volunteers to count the ballots, to staff the polling stations, to guard the ballots and you have a 'distributed compute system' that is highly resistant to tampering. Also, it deepens the experience in the population that 'we as a people' are doing 'our elections' and it works because we can all trust each other, to the degree necessary. Do your elections electronically, and you'll turn the communal experience to a bureaucratic act. Also, the keys to the kingdom will be just one forged access token away, stored on some server.
Every single day for many years now firms, hospitals, and infrastructure has become the target of ransomware, malware, and espionage. Whoever tells you that elections should be 'digitalized' is either stupid, a liar, or both.