Any fee attached to commenting is little different from just banning comments. Few will pay to put their $0.02 on a story they disagree with even fewer will pay if they agree with it. They'll go bitch about it on FB, then bitch about the commenting system too.
As you say, fighting comment trolling and spam is expensive, news media isn't making money hand over fist. I've rarely seen comments add value to a site so why pay to keep them?
The problem is that we are both approaching this as a problem that needs to be solved, while in reality it only needs to appear like one.
Social media companies make their revenue out of "engagement", and posts breaking the rules often generate the most of it, so properly moderating them would actually hurt their bottom line by more than just the cost of said moderation.
These companies are incentivized to leave as much "bad" content up as they can (as it generates engagement) while making it look like they are taking action as to not risk bad PR or legal consequences. Same goes for deterring or punishing offenders - long-term bans are trivial to implement and would significantly deter breaking the rules, but would also decrease "engagement".