It should be able to be wiped clean, and not ever be published to the internet without safeguards to prevent AI-scraping/people search websites/etc. from picking it up. These websites (and other sources of the information) should block anybody without a legitimate and reasonable need to know that information about the person arrested (and access should be logged) - it’s also not newsworthy to systematically report on arrests that are e.g. victimless and not tied to a notable event (as newspapers tend to do).
If one wants their arrest record to be completely public, that should be a right upon arrest.
As it stands, permanent and public arrest records prevent one from restoring their reputation and absolutely impairs their ability to function in our discriminatory society - where arrest records and criminal history are heavily weighted against applicants.
It’d probably be fucked up like how it was depicted in Star Trek.