They are still obtainable, but with the number of people who actually honor at the end of a match, you need to play a LOT of matches on a regular basis to obtain one. I have over 800 teamwork honors and recently lost my honor badge since I haven't really been playing as much for it's upkeep, but was able to keep it for years due to playing regularly and getting about 3 honors a day (give or take).
With how little people honor each other at the end of each match anymore, it might be worth having Riot look at the honor system and maybe make it easier to obtain them if Riot is dead set on keeping it.