Corki should be "magic damage spellcaster ADC",also there are some more "ADCs" that you didn't mention.
(He used to be bot,now he's an ad carry ranged jungler)
And,obviously 
Getting back serious,I say,even if some of them have really similar playstyles,they all have some "specialty" to them.
Slow-based for kiting
Traps and long range crits
as i said,magic based spellcaster. I know he's not used bot anymore,but he is considered still "AD Carry"
It should be "extra gold for more snowball",but with how he's been in recent times it can also be "super damage unless you miss your showoff"
Spellcaster Attack based spellcaster + 2nd Safest + Single-target heavy
Tankiest ADC and Jungler ADC,but low-range
"Death in four or less acts". JK,"Assassin" and "Spellcaster Snipe"
Avalanche effect with kills. Also explosions,i think
As you said,the true embodement of "Glass Cannon AD Carry who needs a support in bot lane". Also "No need to smite,i stacked that baron at 256",i guess.
AS based magic damage ADC,or On-hit sometimes
low range Spellcaster duelist that can shoot you down while escaping.
Bully and combo(ult) ADC
Juggernaut ADC (some people can make it work,and Riot wanted it when they failed it,so technically)
Roam Assassin Burst
Mobility + Spellshield + Hard Push Potential
1st safest + Hard Push potential + Tower Destroyer + decent magc damage + she once used to be the reset based ADC but now she only has a reset on her W but who cares as long as she is used we won't change it. Yes i'm a bit salty that her only reset is on her W,even if it was for balancing purpose that they removed the E-Q interaction.
Assassin + Poison + Invisibility
Magic + CC + Spellcaster
TankShredding + Mobility + Chasing victims + 1v5 + how is she able to kill squishies in 2 hits if she is the tankshredder.
Poke(not even that much like others) + Crit and linear CC.
Anti-Farm Anti-ADC Pro-memes.
I went way less serious than i should've,but i really think that in most cases the "niche" exists,at least a little bit. Obviously there are cases in which it doesn't feel like it's there and should be changed a bit,but i don't think it should be a drastic change such as the pre-season of s5 where a lot of ADCs were changed.