Historically, the question has largely been posed in the form, "what must or can be kept secret?" rather than "what must or can be revealed?".
The general rule is (and has been since before the American Revolution) that anything which isn't required to be kept confidential may be disclosed by the government.
Law enforcement agencies developed a custom and policy, long before there was clearly defined law one way or the other, of disclosing this information. The right to keep an interaction with the government secret has been the exception and not the rule.
Law enforcement agencies had good reason to have a symbiotic relationship with the press and other third parties in sharing information while carrying out their duties. By providing information, news about crimes often got out and caused citizens to report information about crimes that helped law enforcement agencies solve crimes.
This default rule one way or the other didn't matter very much until the last few decades, because the relevant information was highly decentralized, was contained on a single set of paper records that wasn't easy to copy or collate, and there was no one out there in the business of consolidating arrest records in a systemic and comprehensive manner.
Also, prior to the formation of formally organized police departments in the late 1800s, except in the exceptional cases where arrest warrants were issued, records of arrests made in the ordinary course of enforcing the law simply weren't maintained on a systemic basis at all, with the first records in a case usually being the record of commencement of criminal charges in court made by a prosecutor or a police officer or magistrate given the authority to do so.
Concerns about uses of arrest records for improper purposes, and the concern that there were important systemic differences between making decisions based upon arrest histories, rather than based upon criminal convictions, only arose when (1) records of arrests began to be maintained in a centralized fashion by modern law enforcement agencies, (2) technology and the earliest data brokering businesses started to collect and collate these records from many different jurisdictions on a comprehensive basis, and (3) civil rights laws were enacted that cast doubt on the propriety of make decisions in someone's life like hiring or extending credit, based upon arrests that did not result in convictions or arrest records containing erroneous information.
It has taken decades for this issue to gradually emerge to the point where policymakers have seriously started to reconsider the long standing status quo that has existed for as long as these records have been maintained regularly in the late 1800s, due to concerns about the risk of people facing discrimination based upon arrests that turned out to not actually led to criminal convictions.
Other answers have emphasized concerns about making sure that the government can't legally "disappear" people, and allowing criminal defense attorneys to locate potential clients, and those a reasonable policy considerations in 20/20 hindsight as we consider what would be the best policy today. But neither of those considerations was at the forefront at the time that the policy of making arrest records widely available to the general public when they first started to be kept was widely adopted. Those considerations mostly date to fifty or sixty years after this practice came into being historically and established the status quo.
In the pre-World War I era, the legal claim one could make in a Petition for Writ of Habeas Corpus, rather than policies of making arrest records public which often didn't even have the force of written law or regulation anyway, was the main tool to address the problem of people who were "disappeared" by the government without due process or public disclosure.
In countries like Germany (and most of Europe), the status quo was disrupted in World War II, and in the aftermath of that event, as the institutions of government, in general, and law enforcement procedures, in particular, were rebuilt from scratch, the considerations that were at the forefront of people's concerns then were very different than they were in the U.S. in the 1700s and beyond when its law enforcement practices began to emerge organically in a more or less uninterrupted progression to the present. There was no singular event or moment at which the U.S. has ever had to completely redesign its law enforcement system from a clean slate, and the concerns about the kinds of government abuse that people were worried about in the U.S. were different.
Even now, the big concern in the U.S. about disclosing arrest records is about abuses of those information by private parties in economic matters, and not abuses of that information by governmental parties or organized conspiracies like Latin American death squads.
However, it seems to me knowing about an arrest objectively provides
little useful information (at least much less than e.g. knowing about
convictions), because many people are arrested without being guilty,
and many people are guilty without being arrested.
It depends upon what you want to use the information for and whose interests matter to you.
Basically 100% of people convicted of crimes are arrested before they are convicted. Something on the order of 50%-70% of people who are arrested are subsequently convicted of something. Equally important, lots of people who are arrested for something minor have done something that was at least anti-social, whether or not it was a minor crime or justified, and even if the charges are ultimately dropped out of mercy or because the seriousness of the offense doesn't justify the expense of invoking the legal process to charge that person with a crime.
Certainly plenty of people are arrested without any legitimate reason or due to good faith mistakes that are promptly cleared up. This percentage is particularly high if you aren't white, or if you are a young man who is poor or working class. But, maybe that percentage is 10%-20% of arrests. That is a huge percentage if you are worried about individual injustice, but it is a tolerable margin of error if you are engaged in a statistical screening process and care much more about entering into important relationships with people who are trouble free than about justice to people who you don't enter into relationships with, because you have an excess number of prospects which you are having trouble narrowing down anyway.
If you are trying to choose a courier for the a jewelry store, or someone to have access to nuclear secrets, the downside risk of letting someone slip through your background check when they shouldn't is so high that you may be comfortable with some injustice. If you are screening tenants for a $300 a month subsidized studio apartment, the appropriate balance between injustice to applicants and eliminating anyone with the slightest yellow flag of risk may be different.
Relying on arrests can result in unjust treatment of people who are unjustly arrested. But it is easy, comprehensive data to obtain, and if your primary objective is to exclude anyone who might have engaged in disorderly or criminal behavior even if it isn't very serious, so that your "finalists" in an employment application or rental application or background check of a potential spouse, there are a minimum number of such people, and the down side to you of excluding someone based upon an unjust arrest is small, arrest records can provide lots of useful information and indeed can be more useful to you than criminal conviction records which have very few false positives, but have too many false negatives of people who did something but didn't get convicted of it, relative to arrest records.
The question for someone making privacy policies with regard to arrest records (much as in the case of credit reporting) is how to balance to interests of someone reviewing those records in getting maximum power to screen out anyone who might be a problem, against the interests of the person whose records are being reviewed in being judged based upon false or misleading information.
Politically, people with an interest in screening people out have historically had more political power than people with an interest in not being judged unjustly, although this has shifted over time as the scope of arrest records databases and their use has changed, as people have become more skeptical of police good faith in making arrests, and as these tools have been used to focus on high end prospective employees, tenants, etc. rather than to screen masses of ordinary middle class and working class people.
Also, norms about what a person should be entitled to keep private and for what reasons have evolved, in a manner that has given more moral weight to a desire for privacy than was historically the case, as opposed to an attitude that third-parties should be entitled to get all the facts and judge for themselves what they should conclude from those facts.