Why i think the current honor system fails
There are merely two issues that'd I would like to address.
First up, you cannot honor opponents. I think we all agree this is a problem so I'm not going to bother going into it.
Secondly, you can only honor one player. This may not look like an issue on paper, but hear me out:
Whenever I play, it seems like the player with the best KDA gets the honors. This means the player who was most polite or enabled the ADC to get the best KDA will both be thrown aside in favor of the one who got the most kills.
I don't know, when I think of honoring someone, I think it should be based on who was the most helpful and polite person on my team. If you go 30/2/8, good for you, but I'm going to honor the one who gave me advice or communicated well.
Sadly, it seems that most players do not select honor with that mindset. They want to make their one honor count, so it goes to the one with the prettiest KDA.
That's my take anyway.