Are you saying a banned player from playing a game will first need to be reported? A moderator like you, who is reading a game and sees a toxic player insulting another player, I feel like as if the toxic player doesn't only need to be reported by another player and the moderator watching can also take immediate action with a punishment. I've seen on another mafia site players get banned without having to be reported by another player.
The report button exists for that reason. For one, I'm not going to be able to see every single post. That's not realistic. And even the ones I do read, I'm not going to be paying full attention to each one. What this means is that sometimes, I could skim over a post and not see anything that indicates, say, bullying, or an attempt to aggravate a player to upset them.
If a post is reported, I can see it within it's own context, and immediately I have reason to put my mod hat on for it. There's actually no reason not to report posts - this way, if I'm not available, any mod can step in if required and they don't need to be reading the game for it. Every player, user even, should be reporting posts that the feel needs moderator action. That's the point of having the report function.
That does not mean that the only time action will be ever taken is if something is reported. It simply means that if you feel somethi g needs addressing, as in you take issue with what is said, the report button should be used.
Generally speaking, my first inclination is going to be "can I diffuse the situation", so if I'm active at the time, I might give a warning for example. If I come back and see it's reported before I've addressed it though, then my reaction will likely be different. Because more time has passed and now it needs mod intervention that goes beyond just diffusing. Sometimes, a player will say something that could be objectionable, but the player on the receiving end has no issue with it, or appears to take no issue with it. In that case, unless what is said is egregious, there's a fair chance it will be overlooked, or left at a soft "watch it, this is a bit much". By the player reporting it, I now know that they have in fact taken issue with it, and thus it needs addressing more firmly. This helps to remove the ambiguity - no one wants moderation that intervenes over banter, or something that isn't an issue. So again, this is why it's important to use the forum features for this stuff.