Here's the thing: no one's going to do anything about it, but technically this may amount to libel.

On reddit you're banned via private message, so no one knows why you'd been banned, even if the reason is bogus. If someone accuses you of something in a comment, you can defend yourself. You have the right to reply. But in the fediverse you're banned and if the mod does it for a made-up reason, that false reason is publicly viewable in the modlog without you being able to do anything about it. They've maliciously damaged your reputation without any recourse, right to defend yourself / right of reply.

Now imagine at one point their username is linked to their actual name. An employer does a google, finds they've been banned for homophobia. Some arsehole doxxes them, and sends a picture of their being banned for homophobia to their employer. They're fired for allegedly being homophobic on social media. At that point, a good lawyer could potentially prove libel and damages caused. You're clearly annoyed OP. Now imagine someone with too much time and money on his hands.

It's real amateur hour shit. Sure being sued for libel is incredibly unlikely, but there are only downsides to not erring on the side of caution with stuff like this. Want to ban someone? Make up a generic or non-defamatory reason, or simply call them a dickhead, and go on with your day.

Stuff like this, the failure to respect GDPR/Privacy and NetzDG laws, a failure to properly deal with CSAM material... it's a ticking time bomb under the whole fediverse.