On the topic of the actual question Doc asked... bans not necessarily lasting longer than a decade is definitely a thought worth considering. I personally have suffered under a ridiculous stigma from two decades ago paired with a cruel culture of harassment that assumes that people never, ever change and digs up ancient dirt under this principle. I was so jittery when I first joined Creeper's Lab in large part because of suffering under years of this and having no idea where else to go. I would go so far as to say that this isn't even uncommon -- I just was shell-shocked from a particularly malicious example of the general rule that there is no forgiveness on the Internet. As brutal a statement as that may be to make, in my observation it's true.
The main thing that tends to concern me when it comes to bans here, though, is that we aren't necessarily making it absolutely and immediately clear what the rules are, what the rules mean, what the rules are there for, and how strict each rule is. While most of this information is available, people have to go digging for the majority of it, and that idea may never even occur to them. People getting abruptly, permanently banned for reasons they don't actually understand isn't fair or just, especially if it's less than ten seconds after they got a warning. Heck, we don't even make it clear that permanent bans are practically the only punishment we employ; the sheer harshness has unquestionably blindsided people. Efficiency is not a virtue if it comes at the expense of justice, and oftentimes it just takes another fifteen seconds to do things right (like, say, responding to someone's idea of a greeting being "what up *****s" by actually giving a warning for language and seeing whether they say "sorry" or "make me *****" before banning them).
Some staff tend to treat all offenders as though they were college freshman frat boys, old enough to know perfectly well what they're doing wrong and reveling in their ability to do wrong. Sometimes, that's clearly the case, and those cases tend to be very obvious. However, Minecraft is a game also played by young children, many of whom have never heard the term "griefing" before, let alone been introduced to abstract concepts like the tragedy of the commons. A rare few are even clearly so young that "mine", "not mine", and the difference in how you treat each are still concepts they're working on in general. Heck, Sesame Street regularly talks about the concept of sharing as though it were novel for a reason. I can't help but imagine that some of our bans leave little kids sobbing; as a sufferer of childhood trauma myself, I don't like the idea of our staff inflicting even a lesser degree of it. (Heck, I remember one time when after a ban, an angry parent came on insisting that their child didn't know better due to autism, and got exactly zero sympathy from the staff.) For all our talk of the server's language rules being for the sake of children, we don't do much of anything to help children themselves play by our rules.
When it comes to block-breakage-based griefing for the sake of obtaining early resources (which is to say, the typical kind), I think it would be clearer what we're telling people not to do if the first warning came packaged with a tiny dose of mining fatigue (say, 20 seconds). This would give them time to make sense of what was said, release the mouse button, and move elsewhere. More generally, "What's griefing?" is a question that we should encourage and answer, not ignore as though people were playing dumb; after all, it is our strictest and most foundational rule, so we can't afford to have anyone get it wrong by accident. We also have a tool that we're underusing when it comes to people who don't seem to be listening to staff instructions on Cimmeria -- Twixxi's bee prison.
There's also one rule that's clearly unwritten: don't ask for ops. This is a special case of every instance of it being treated like it's necessarily coming from a hooligan rather than someone who doesn't know better. I've noticed at least a couple of cases that were clearly the latter -- generally on the assumption that "ops" equals permission to play normally on a server that clearly doesn't give you that permission automatically, not dangerous godlike powers that in the wrong hands could be used to ruin the server. The first resort if people ask for ops as if this were just a normal question should be to say, "no, ops are for staff only", not "sure, type /pmc" as a prelude to a ban. ...If they keep asking for ops after being told no, or are more obviously trying to enact a scheme in the first place, then we should hand them the schmuck bait.
Further complicating things is that some people come here after seeing YouTube videos of servers with very different rules than ours, or just come from anarchy servers to begin with; the idea that a different server might have different rules is not necessarily immediately apparent. It reminds me very strongly of how some roleplayers and roleplaying subcultures have trouble with the idea that there are different kinds of RP and different things one might want out of the experience. (Of course, some just don't respect that we have different rules than they want, and that's a whole other thing and worth a swift kick in the rear.) The tutorial helps somewhat on this front, but I'm not sure how many people actually read the signs rather than just barreling through it at top speed for the rewards -- particularly among younger players. Furthermore, a number of people get banned before even getting that far, such as by being banned for repeatedly punching things in the lobby. There is, after all, a reason why I have suggested making it so when protections trigger reversion of damage in the lobby, the offender gets smacked by mining fatigue -- particle, sound effect, and all. It would make it a lot clearer, in a nonverbal way, that this isn't OK -- or at least prompt a "what the heck?!" so we can explain it ourselves.
Concerning the concept of appeals, it does seem as though a more formal appeals process might help for situations such as the one of allegedly attempting to fix a broken machine and not expecting to be banned for it that happened this past weekend. I've seen at least one attempt to appeal a ban go by unnoticed on the forums, as well. A formal appeals process would, however, come with the cost that the number of entitled jerks appealing would far outweigh the number of cases of honest mistakes being appealed; inevitably, frat boys are going to be more tech-savvy than young children.
Finally, I unfortunately feel it necessary to point out that banning is not a competition. There is no prize to be had for being the first to bring down the banhammer. Your ban count is not a score to be proud of. You are ruining another human being's day; be absolutely sure that person's day actually deserves to be ruined. "Bans are bad" is more than just rhetoric to be recited because Doc happens to be online.