There's a few misconceptions in your question that addressing might help things out a bit.
Misconception 1. Reasons for suspensions must be kept confidential.
This isn't actually true. Moderators can't share the information with third parties of their own accord (e.g. on meta) but they can share an explanation publicly with the permission of the person who was suspended. While this often requires the suspension to be over so may not apply in your specific example, there is certainly opportunity for users to talk about their own suspensions and ask for public discussion.
Misconception 2. A lack of a public account is less safe for suspended users.
This is a huge misconception. While there are some risks, in the vast majority of cases having a public account of suspensions is more harmful for the suspended user's ability to rejoin the community after a suspension than keeping the reasoning private.
- If a user was suspended for sock puppeting and falsely inflating their own reputation, this being public may lead people to continually distrust that their remaining reputation was earned fairly.
- If a user was suspended for harassing others and their comments were retained publicly in some sort of record, those comments could perpetually make them look bad for all time, even if they'd significantly changed their behavior in the time since.
The other side of this is that a public account could continue to harm the people targeted by the suspended user. Even if not mentioned by name, having a permanent public record of the harassment they'd received (potentially revealing a complaint from them to the moderators as "evidence" of the person's harassment), they'd potentially never be able to move on from it, either.
The reality is, in most cases, lack of a public record is better for the suspended users and the people who may have been harmed by them (if any). Keeping this private allows everyone - the suspended user, the harmed parties, and the community as a whole - to move on from the past without being judged by it.
Misconception 3. There is no oversight or opportunity for redress of suspensions.
This is mostly implied in your question but it's worth bringing up. Suspensions may be private from the general users on the site but they are not private from the other moderators on the site - all mods receive a special inbox notification any time a mod message is sent to a user, so any mod message (and suspension, which requires a mod message) is visible to all moderators on the site. While they may not be reviewed by all mods, on most sites, these get reviewed by any mod who's around.
Users who are suspended have the ability to respond (once) to the mod message to ask for more information or explain what happened or why they acted the way they did. While this may not cause their suspension to be removed, it's an opportunity to communicate with the moderators to better understand what's going on.
If they attempt this and don't get a reply or they don't believe that responding will be of value, users can always contact the CMs through a form on the /contact page. We even recently updated the form users can fill out for this purpose to make it easier to collect the necessary information from the user so that we can investigate the situation.
We often get such contacts and we investigate them with as open a mind as we are able to. Over the years, many users have come to a point where it's very difficult to feel some sympathy as they have repeatedly caused drama either on specific sites or across the network - but we do our best to investigate any communication that comes to us with enough information to actually look into. Most of the complaints we get are just that - "moderators are evil and I'm innocent" - with no actual explanations or attempts to help us understand their situation.
I'd argue, as a former mod and now as a CM, that most moderators are underusing suspensions, not abusing them. I've looked into several situations that came to us in this way and in most cases, I find that moderators have generally given people more chances or been more lenient and they only suspended when there seemed to be nothing else they could do.
Third party users can also use the contact form to reach out to us to request an investigation but they will not receive any details of the outcome, or even whether an investigation will be done.
Misconception 4. Everything that happens when someone is suspended can be made public.
This is based on an extension of your questions - essentially, if you're arguing that the reasons for a suspension should be public, that implies that you believe that all elements of a suspension can be public... but they often can't.
- Some suspensions come about as parts of investigations moderators or staff do that must be kept private as they would otherwise reveal how some of the tooling we use works - as well as potentially showing off some of the shortcomings of those tools.
- Some suspensions come from private interactions that would potentially cause harm if they're made public. For example, if someone has been emailed by a user with content that is abusive or threatening and that person reaches out to mods or staff privately to ask for help, that may end up with the user being suspended but that should not be made public, as the person being harassed could continue to be harassed as a result.
So, all-in-all, I feel that it's better for the community that we maintain this process. I believe that there are sufficient checks and balances in place to allow users who feel they were unfairly treated to request redress and even ways to bring the issue up publicly once their suspension period has ended.