The two main benefits I’ve seen of private trackers are that you avoid the issue in the OP which happens all the time on public trackers, and that shows download in seconds.

Not sure how helpful they would be if things weren’t automated. I just have things set up so my Jellyfin users can request shows and they get downloaded automatically.

But with that said, “private” doesn’t mean it costs money, just that it requires an account (and usually that is an application process). It means they can kick people off for uploading things they shouldn’t.