I doubt they would have the time for it
You're right. We wouldn't have the time for that, certainly not with the activity level of this forum.
You seem to think things would change for the better with this approach, but given the same forum rules you'll see 99% of the same posts you don't like. It would only be worse because NOTHING would happen on this forum unless a mod is online and actually we aren't at all times, we do have lives to live.
This is a forum where pretty much any opinion is allowed and only a couple of general topics are not allowed to discuss (politics and religion). It's only natural that there will be strong disagreements, that one side will think the other is a complete moron and shouldn't be allowed to post. Well, the admin and the mods value free speech, this is just a consequence of this freedom. It's a far lesser evil than restricting opinions which would just simply kill the forum in the long term because the mods would be viewed as tyrants if we did decide such matters.
The best way to mitigate trolling and bickering is through the reporting system. We rarely respond to a report, but every single one is viewed by
at least one mod. We as mods don't read every single thread and post all the time, as I said, we have lives. If everyone knew the rules well and reported stuff they thought violated the rules, then you'd contribute to raising the quality of this forum. I know stuff slips through the cracks here, the violation is there, no mod happens to read it and nobody else bothers to report it, so it stays like it's ok even if it isn't.
Trolls are everywhere until you have the responsibility of making sure a troll really is a troll and not some incredibly clueless dude legitimately in need of help, this isn't as easy as it might seem. Some guys really just are that naive, even if you aren't. Some guys are also just trolls, but they'll become obvious to us mods sooner rather than later anyways.
I totally see the problems you're mentioning, but I don't agree with your solution. As it stands we don't receive as many reports as we probably should, so I suggest reminding yourselves to report whenever you see trolls and bickering. We usually do get around to it rather quickly.