I play 3v3 now and then however i feel that why lots of people don't play 3v3 is because there is no ranked. Yes, there is 3v3 ranked teams however, not many people want to play ranked team. Things I hear about lol a lot is that there is only one map that is really played because, its the only map with ranked. I know not as many would play compared to 5v5 however it would only add to the game i see no way that it would hurt the game.
Reason why ppl don't play 3v3 not because it haven't ranked. 3v3 unfair and unbalanced map. Thats why.
There's two reasons why people don't play TT imo:
There's no real reward. When you play summons rift, what do you get? A ton of XP, IP, and Mastery Points (Which adds up to the mastery emblem over your character). What do you get when you play TT? Lower amounts of IP and XP, ad no mastery points. So there's no real point in that reguard.
(And this is the big one) They never promote it. Thing about it, what do all the pros play? Summoners rift. What do all the featured streamers play? Summoners rift. Where does everybody therefor play? Summoners rift. This is with all of the gamemodes. It doesn't matter how many updates or visual updates that riot gives to these games, if they don't properly advertise it with featured tournaments (if they can do it with a featured gamemode like URF, they can do it for a permanent gamemode like TT) or give uneven rewards for playing
This goes wit every other gamemode too. However, for Aram, I can understand, since you're forced to use other characters and would get chracters you usully don't end up playing in the first place.
