Without any tangible rewards attached to honor, a lot of players seem to just ignore it now. Also, from my understanding, the icons are rewarded not for flat numbers, but for being in the top x% of honored players on the server. Last I heard, players in bot games are apparently much more statistically likely to reward honor, so most of the crests don't go to people who are primarily playing PvP SR.
Honor was a cool idea, but I think it's hard to make people care about it. Serious rewards would go a long way, but they would also encourage honor trading (you give me x, I'll give you z), which kind of defeats the purpose of honor in the first place.
I don't play DotA, but from my understanding, you can end up in some kind of "dishonor hole" (dunno what it's actually called)... if you get reported too many times, you start primarily getting matched with other jerks. Maybe Riot could do the opposite--players who receive a lot of honor are more likely to be matched with other honorable players, at least in normals. This would make honor meaningful, without incentivizing honor trading (you want to only honor players that you would actually like to play with in the future).