It's because it is transparent and can't be altered. That's the reason why blockchain has a better integrity if you're for that and projects that are into it aren't just for crypto but also for main use cases like voting.
A blockchain-based architecture does not have "better integrity" than other approaches per se--just ask one of the thousands of people who have lost
billions of dollars on failed blockchain projects. Blockchain can fail just like any other computer system can fail.
You're defining failed projects compared to the working projects. Talking in general about the function of blockchain, the integrity is there. Of course, you'd look at the failure of blockchain when you're defining the specific projects that have failed. Blockchain isn't just all about crypto nowadays, there's the actual use case in different fields aside from crypto.
And no country is actually using blockchain for voting, which would be extremely stupid if they even tried it.
It's just one of the many use cases there but I've found this for that specific.
It might surprise you to know that the US has already used a blockchain electronic voting system to vote in the 2018 midterm election (West Virginia) and the 2020 Presidential election (Utah County).