If moderators can view it without being harmed, what makes them so special?

I can't tell whether you're trolling or serious...

It's not about moderators being harmed or not. It's a preference of the wider community to not have the harmful content, and the moderators volunteering to help keep it that way.

With most harmful content, the effect of seeing a single instance is not significant. Being exposed to it constantly in places you frequent for other reason (your online communities, or advertisements everwhere), builds up much more of an effect. Now moderators being constantly exposed might also be affected, but they're choosing to do so, and may have coping strategies in place for the more extreme cases.

Online communities can moderate as they see fit. I'm not talking about that, I'm talking about the law banning certain content.

I've lived long enough to see certain kinds of content banned, and then embraced, and then a different kind of content be banned.

Which era is correct in their choice of banning?

What's the deal with trying so hard to defend the advertising of an objectively harmful industry?

I think a good parallel here is Tobacco advertising. Smoking is harmful in every way, therefore I don't see any reason why advertising it to a broad audience (which will inadvertently also include children) is something we should allow.

What's the net benefit of allowing such advertising? I don't see it. Yo could argue something about rights to free speech or some variation, but societies still have a responsibility to look out for the health of their people, no?

I agree that children are special and should be protected.

As for adults, I am an amateur historian. History is jam packed with censorship of things those in power have deemed "harmful". Examples:

1. William Tyndale was burned at the stake for translating the Bible to English.

2. Galileo was put under house arrest for his heliocentric views.

3. Mae West was sentenced to 10 days in jail for her play "Sex".

4. Boris Pasternak's novels were banned in the Soviet Union.

5. TV shows in the 1970s were not allowed to show toilets in the bathrooms.

6. Homosexuality could not be portrayed in films until the 1960s.

7. Howard Stern was fined $2.5m for "indecent" broadcasts.

8. Violence on film is far, far more graphic today than was allowed just a few years ago.

9. You can say "fuck" on TV today, along with nudity.

And on and on it goes. Those censors were just as convinced as you are that they were doing the right thing.

Yeah that's true, random unrelated things did happen in the past, but that's not a credible argument against having slap on the wrist fines for advertising gambling.