Mods make mistakes too. There is nothing wrong with genuine appeals.
No doubt. The problem is that Meta is being overrun with ban appeal threads. I don't see why a child board can't be created. It's not exactly like it would require more moderation--it's just like putting a partition in place where those members who don't feel like looking at plagiarist begging, lying, and general nonsense don't have to look at it.
No, some cases need a bit more investigation. Lately there was one account banned by mistake.
Yep, I saw that and I've seen others, too. I wouldn't argue that people shouldn't be able to appeal their ban, just that such cases like the one you mentioned are the exception, not the rule, and that most ban appeal threads are just a bunch of excuses and pleading by people who know exactly what they've done wrong. If you create a child board, you can then put it on ignore if you want.