The goal was to make the player base less toxic.
I think you might have a pretty major misconception here. The goal of the reworked Honor System wasn't to make the playerbase less toxic, it was to more properly reward the more sportsmanlike players of the community.
What is meant to make the playerbase less toxic is the Punishment System/Instant Feedback System (IFS), which, while may be some issues with it (automated system involving an objective, closed-off look at a single person's behavior regardless of circumstance is a pretty hot topic as it is), does do its job to punish unsportsmanlike players.
...and at the end you don't feel like honoring anyone.
And that's perfectly fine. If you feel nobody on your team was sportsmanlike or deserving of an Honor for any reason, you can skip out on it.
The honor system has failed to meet its goals.
If we're going by your assumed goals of the Honor System, then yes, it has failed. But, if we're going by Riot's stated goals, then, I'd say that it hasn't.
Give me a ban list where I can prevent being matched with that player on my team for a period of time that times out but accumulates if I match after the timeout and they are still nasty.
While an interesting concept (and I'd personally love to have my own "keep me away from x person" button), I don't think it would ultimately help in the long run, because:
- there are some people who would just plain block anyone and everyone.
- it increasing in duration if the blocked player proves to be toxic in further games would be either confusing (how does the game know they've been toxic further down the road?) or redundant (if using the IFS to identify toxic behavior and extend the duration, the whole concept may eventually, on its own right, become useless, if the toxic players are getting banned for their behavior.)
Those are just two problems that I have about it, and - again, while I would like a block feature of some sort, I know I can report and rely on the IFS to do the job for me, since there's several hundreds of players in the game, and I'll seldom get matched with the same one twice.
TL;DR: The Honor System's goal wasn't to reduce toxicity, but to reward sportsmanship. It's not mandatory, and, of course, it's not perfect, but you really aught to look more at the IFS than the Honor System if you want to see toxicity being dealt with.