Its easy to disregard tone when its somebody else's feelings at stake, much harder to look past tone when its your feelings on the line. Nobody is above the fray.
Maybe we need a robustness principle[1] for human communication. Be conservative in tone you send out, liberal in what you accept.
> Note that Crocker's Rules does not mean you can insult people; it means that other people don't have to worry about whether they are insulting you.
Your tone still matters unless you are communicating with someone else who is operating under Crocker's Rules.
While I like the idea of that in theory, I have to say I think it's operating on the somewhat flawed premise that tone and other flourishes offer no informational benefit. I view tone as a "hint" for the context of the surrounding statements, and as such, it can alter the interpretation of them. This is useful for efficient communication.
I think Crocker's Rules will help people will communicate the correct information efficiently, but I don't think it's necessarily in the minimum amount of time, just a better average case time. It's probably very useful in situations where the shared social context of the communicating parties are distinct enough that the hinting provided by tone is misinterpreted, which can be common on the internet, where disparate cultures clash and there's no visual channel to additionally help communication.
For a very simple example, tone may convey confidence. If that confidence is in a statement that people find reasons to doubt or disagree with, depending on their own confidence they may feel more or less compelled to disagree.