To be honest, I want to correct misconception of people who think there is meta of supports going bot lane. Yes supports are going bot-lane, but not-only supports are. Actually most of support-role champions are not made out of supportive dough. Reason is simple. What LoL community qualifies as Support is slightly different from what actually should be definition of word.

There are two things called support so let me differ between them. Support as role and Support type champion.

Support as Role

"Something is played as Support." - how one talks about role of support. As shown with support Annie, trends can change with changes of itemage about what can and what can't be played as support sucessfully.

Support as role is about feeding your adc and protecting him. It is standartized name, but one could argue secondary bot laner or caddy would be better name. Being support as role is possible for many non-support champs, because it consists of controling vision, protecting carries and having cheap items one can efford with low gold income. And because there are lot of supportive items one can afford with low income, one does not have to be support type champ to play support.

There are few things champion can offer to become good support-role.

Supportive Power

Supportive power is about amplification of allies by either making them stronger or decreasing power/resistances of enemies, healing allies, or shielding them. While many secondary bot lane champions have bit of Supportive power, it is not necessary(Velkoz and Zyra for example can support without having one bit of supportive power).

This is what defines support, but there are other things that are really good in bot-lane while not being of supportive character:

(Long range) harass

Harass is about making enemy lane low on hp, trying to force them out of lane. This can give your lane strong advantage when you go for all-in, but again, long range harass is not necessity. While one could argue if Thresh hook damage can be called harass, I believe we can stop joking and accept its power is not in its damage, but in CC. So there are few supports, who can live without real long range harass.

Crowd control/Displacement

Agressive crowd control/disp.

This is probably most key thing for current meta secondary bot laner. Most of ADC's do not carry their own CC or have it somehow restricted(only on ultimate, or Vayne having to push target into terrain), but they synergize well with it(they do lot of damage, so if enemy can't escape... you know the rest). While there are few exceptions(Ashe, Varus), having slow or root or even stun is big plus for bot lane. Looking at Blitzcrank, who is all about pull and knockup(+ silence and damage of ult), you can see that one can be good secondary bot laner with almost only thing he can provide by himself being CC. Agressive CC can be of course used for peeling as well.

Peeling CC/Displacement

Peeling CC is mostly inferior to agressive CC, as agressive CC can be used to peel almost always, but peeling cc can be used agressively only rarely. To define Peeling CC, we need Janna. Janna is unique champion made of supportive power and Peeling CC almost completely. Her abilities have low damage, making her harass subpar. She is also one of few champions who can live without having agressive CC. While ult and Q can be sometimes used to single out champion, it is mostly by wrong positioning of player and not by nature of said spells. Janna power is not about feeding your carry, but about protecting his farming phase and complete denial of any all-in against him.

Vision control power

With S4 vision changes, vision items triumphed over vision abilities. While it could be theoreticaly part of secondary bot-laners kit, right now, only support Oriana and support Nidalee(if my memory serves me well), both quite disputable have something like this in kit. Or, support Ashe(hehe). Or Thresh(but using Lantern is only good for checking, not for persistant vision control).

Support type champion

"Something is support." - how one talks about supportive traits of certain champion. These supportive traits only change if champion himself is directly changed by Riot.

Support type champion is champion, whose kit is built mainly around support power. Prime examples would be primary Soraka(heal, mr debuff, silence and one more heal), Taric(armor aura, armor shred, AD/AP aura, and heal), Sona(on-hit powerup, heal, shield, speedup, damage reduction) and secondary Nami(MS buff, on-hit effect, heal) and Janna(MS buff, heal, shield) who also have strong CC trait in their kits(Stun, slow, + ulti for Nami, knockup, slow and knockback for Janna). While other popular support role champions like Leona(passive), Thresh(Lantern) and Alistar(Heal) and Morgana(CC-shield) might have one or two support traits, their kit is based more on using CC or doing damage.

Support role champion is not same as support type champion

Why? Because of supportive items. Meta expects support role to control vision. That can be granted by itemage. Face of Mountain, Locket of Iron Solari and Mikael's Crucible provide supportive power to champions who lack it in their kit. But you could build these items on yasuo as well...(not that I would recommend it though).

Support role champions in current meta do not have to be support type. There are CC-caries like Leona, Morgana and Thresh out there, ruling on top of "support role" ranks, while not having supportive type of kit. So, if one says Leona is not support, ask yourself - does her kit allows her to heal her allies? Does she buff teammates and debuff enemies? No, she clearly is not support type champion, she has only supportive peck in her passive. That does not mean she sucks as secondary bot laner(actually she rocks down there). But she is not support type champion, and she will never be.

I am not saying support champs are not meta in botlane. I am saying there are way too much - non-support champs who are good secondary bot laners to say - support champs are meta of secondary bot-lane. If in 95% cases, people played 17 champs in midlane and out of them, 2 would be assissins and 15 mages, would you say it is assassin-mid meta?