That doesn't mean everything needs to go through the courts; it means that if your process allows something that Anglo common law does not allow, you should have a good answer for why that is. Does it allow anonymous accusations? Is the accused allowed to know the charges against them, before a finding of guilt is rendered? Is there a presumption of innocence? Is the accused allowed to have a trusted third party - one who knows the rules of the game - to advocate on their behalf? Who, exactly, is responsible for deciding matters of fact vs matters of "law"? Is there an appeals process to fix possibly incorrect decisions?
Going by the linked document by Valerie Aurora, a good Code of Conduct allows anonymous accusations, the accused does not get to know the charges against them before a finding is rendered, there is no presumption of innocence, the accused does not get a third party advocate, matters of fact are necessarily decided by the same committee that makes the rules, and there is no appeal process.
This doesn't mean that such a committee will always do wrong. But I think it's worth thinking about how people operating in bad faith (either on the committee, or reporters to it) can abuse those features to achieve goals that are not actually aligned with what the Code of Conduct is trying to do. Yes, it's true that people can't be put in jail for these sorts of things, but a poorly-run adjudication process can have significant negative personal and financial effects on people.