Earlier this year, in the beginning of season 7, Riot released the flex queue for 3v3 making it so that everyone could play ranked 3v3 and not only ones that had a full team. This was probably the first noticable attempt Riot had made to push the general playerbase to at least try it out ever since they went from the old Twisted Treeline to the new one. (Like seriously, the last patch they even touched Twisted Treeline on was 5.11) I don't have any statistics on how this flexqueue affected 3v3 but in my experience there are more players playing 3v3 now than before.
Now let us dive into the topic of this discussion; why do Riot actively exclude 3v3 from the quest system? There are a lot of people in the 3v3 community that exclusively play Twisted Treeline and doesn't care much for 5v5 at all and making quests that, as an example, says "Win five PvP Summoner's Rift games" or "Win four Summoner's Rift games with 100 minion kills" it really excludes a whole community inside the game and I think this is the opposite of what Riot should do. Riot should rather encourage people to play 3v3 than to force away players from it.
Please consider us next time Riot,