That's a big post. :) Let me try to answer a few points in no particular order:
Community moderators have no power over game pages. In your games' comment sections, you are king. Site admins can intervene, but I'm not sure how reports reach them.
Now, if you delete a comment with replies, it hangs around until purged, so that replies remain accessible. That way you can get rid of the really bad stuff without disrupting the rest of the conversation. Also, if admins suspend a user, any post they made anywhere on itch.io is automatically hidden by default.
For more flexible moderation, you can enable a community instead of comments for any of your games. (Comments will be hidden and become inaccessible until you switch back.) Within a community, you can hide or archive any topic, and if you enable categories, the so-called directory mode, you can also ban people more flexibly. On the downside, now you really are king and all reports will go to you. So you'll need to contact support explicitly if someone is being disruptive in multiple communities, making new accounts and so on.
All that said, we also prefer to hide topics and resolve situations in private, but ultimately you're in charge of your own game communities and can do it your way. That includes adding to the site-wide community rules, or choosing what and when to enforce. Hope this helps!