Even if the old Honor System, where you could honor opponents at the end of the game, was effectively a placebo at the end of its run, I honestly believe that it helped encourage better behavior and sportsmanship between both teammates and opponents alike. Whereas you weren't constricted to one honor a match and you could honor your opponents, there was more encouragement to not throw out unnecessary BM. I remember starting matches with GL;HF's- first to get honor, but then it just became habit. Then when the system swapped over, I didn't feel any of the same encouragement to do any of that, because at the end of the day, the one honor that players get would be to either their duo/premade or the person who performed the best, regardless of actual behavior unless it was egregious.
I think the system's rewards are great, but I don't think that the system is being used for what it was meant to be used for. I believe that the old system accomplished more for curbing toxicity as an incentive, even if the incentive was essentially just a metric. Adding scenarios where more than one person can be honored, and allowing for at least 1 honor for opponents, would do heaps to encourage good sportsmanship.
I'm not expecting it to be the panacea for bad sportsmanship, but I think I'd see more instances of good sportsmanship with a few of these changes to the Honor System.