We have supports that focus on buffing,tanking,healing,crowd control etc. What about one that just weakens enemies. Stuff like shredding armor/mr, decreasing ad and ap, maybe even stuff like reducing crit chance ,temporarily stopping all forms of healing and making enemy cooldowns longer. Would be pretty cool.
debuffs are incredible demotivating to play against which is why its basicly reduced to exhaust.
yeah they're called all inners
because if its not a skill shot its horribly OP.
and if they get behind they're very lackluster.
and if they have literally 3 or 4 debuffs then its incredibly hard to do anything but that specific support job.
they're typically hated more than liked because it usually doesn't pay out, and when they do they end up with all the kills and its really just an ap bot lane.
Look at Lulu's kit again. Seriously. 
The most powerful debuff is greyscreen
You can place that on a champions ability but its too weak to build a champion around - hard CC will be better every time.
The theme of a debuff support is interesting, but it needs to be implemented very carefully, as often debuffing an opponent just ends up disincentivizing them from fighting at all. Having effects that weaken enemies, but also encourage them to attack (e.g. "you are drastically slowed until you attack an enemy champion" or the like) could perhaps be the solution.
There is already excess of CC bot type supports, CC is a debuff. Riot just chose to go heavilty into CC only because it is the easiest form of a debuff to appreciate that does not require any deeper game knowledge. Low elo players do not have the game knowledge, they want to feel good while playing their champions, they would not appreciate a stat debuff as much as high elo and majority of player base is low elo/unranked. If riot discouraged that player base from playing the game they would make less money.
The thing about Debuff sup is that if Riot ever made a champ to be specifically to debuff enemy team it will be a pain to balance since that champ should never be able to get ahead since one team would already be behind and that ONE champ can just keep them like that for the rest of the game
"In some early concepts, we considered making Taliyah a “spite” mage, a cruel sorceress who slings curses and hexes (and otherwise bad vibes) at opponents. Curses on you, your children, your couch, etc. Some Rioters are pretty amused by the idea of a permanently-salty champion, but we'll have to revisit it at a later date."
- they exist as off meta but they exist... oh yah WALL!
?
Her passive is very muddled though, but it does indeed debuff.
support is partially a debuffer, with his ranged slow and armor shred.
Same with support 
with his ult shred, Q AD debuff and slow.
can possibly lower enemies' damage with her power chord.
There are other champiosn who can debuff enemies, 
's W and E, 
ult, 
's W
But yeah there's no real champion dedicated to debuffs if you don't count CC.
Old Raka.
Trundle.
Abyssal Scepter before the MYMU.
Fiddlestick's old passive.
Debuffs in PvP only create anti-interaction and so-called "antifun" that there's hardly anything to play against that other than "tough luck he picked X so he wins".
