Some specific answers and some personal opinions:
I am one of those unlisted mod's. It is MY choice. I am not here often enough to consider myself able to take on an "on-call" function. I read only a few boards and consider those to be my primary modding responsibility.
Some with the mod tools are still deciding if they wish to accept the role or not. The tools are given to certain members and it is up to those members to decide if they will "activate" their role or not. I'm personally still squishy about it, but I do what I can. As long as I'm unlisted, I feel I have the option to retreat from duty if I need to.
The 4 that are listed aren't so lucky.
The current moderators had no hand in writing the rules, but feel obligated to enforce them as written. That doesn't always come out fair, even to our eyes, but when given the tools you aren't asked if you like the rules, you are simply asked to enforce them.
There are no mods that read absolutely everything on this forum. It would be impossible. Some transgressions are going to be missed. And some might be allowed for if a mod is aware of a posters background, and sincerely believes the poster is trying to learn to play by the rules. A lot can be set by how a poster chooses to respond to warnings and suggestions. There is nothing set that a warning needs to be given at all; a warning is considered a courtesy. Someone who is responsive to that courtesy is going to be shown more courtesy back than someone who isn't.
Every mod does this without pay. In our "free" time. When members show some respect for that, they get more respect back.
One rule is simple: multiple names are not allowed without specific, before hand, permission. Change a name or come back with a new one, it gets banned.
I, personally, believe that laying it all on out there is the best approach. But we don't always have the time or the patience for it. And there may be times we've been instructed not to, for various legal reasons. So this is my best effort on openess. For now.
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Mom to an amazing young adult AS son, plus an also amazing non-AS daughter. Most likely part of the "Broader Autism Phenotype" (some traits).