The IFS does not get triggered unless someone is reported and it learns what is toxic from those reports (machine learning). If someone is not reported by anyone in a game, he can be extremely toxic all he wants and there wouldn't be so much as a black mark on his account.
if the system doesn't detect any toxic behavior, then player's honor progress should be faster and they should receive more rewards.
The problem with your suggestion is that the IFS would have to actively and automatically scan every single game regardless if the 10 players are reported or not to see if there is any toxic behavior or not. This is not how the IFS current works or should work. The idea that everything you typed is scanned by the IFS whether you are reported or not is likely not something the player base would want. At that point, there would be no need for a report system and we will truly be in a draconian (big brother surveillance) punishment system.
Conversely, if they exhibit some level of toxicity, but not enough to warrant a penalty, their honor progress should be slower.
This is already how honor progression currently work provided someone is reported.