That's how people get disappeared in failed states.
It's perfectly fine to force the state to clearly declare whom they have detained and their reasons for doing so. We also need to recognize that arrests are very often preposterous (or worse, retaliatory) and not hold it (absent other information or further proceedings) against people.
The fact that someone is in custody should be always available. But it should not be up to Joe Random to pay $11 to my State Patrol to find out why I was arrested last week, especially if I wasn't charged.
(and even if you were able to change the nature of reality as you suggest, why accommodate the state's desire to deny such an action after-the-fact?)
Now there is no absolute guarantee that, if someone has the information, and they are legally required to delete it or not use it, that they don't break the law. But it works in the case of balancing the need to avoid people being disappeared against preventing dragnet misuse of arrest data by employers and landlords. Maybe organised crime employers would systematically break the law if maintaining a database illegal, but they also probably don't mind people with arrest records.