Ones you played 
a fell times you come to the conclusion he really need that asp buff. It helps him on more than one way:
- Helps his splitpush
- Helps his waveclear
- Helps his dps on extended fights
- Helps stacking his passive faster
Graves already has great burst. By further increasing it, you will just decrease his counterplay in that area while still further decreasing his weaknesses what he already has plenty in his arsenal.
Additionaly, Graves is a AA-Caster!!! Not a AD-Caster!!! Their is a hugh differents between the 2. This is what defines Graves as a adc. If you don't auto attack with Graves than man. You really don't known how to play him and you missed about 50% of his damage output.
Graves is actualy in a good spot right now. After the nerfs towards 
he recieved some more play. If you want to put him in a tier list I would place him high in the tier 1 list. This is the main reason why whe don't see any changes on Graves right now. Despite the new season hit him a little bit.
If in the future Graves need some kind of buff I would go towards changes to his Smoke Screen. This is litterly the only ability that holds him down. A change that could be intressting their is further increasing the projectile speed from it. Currently any player with a little bit brain & reaction time can dodge it what really hurt Graves in my opinion since while this ability is not effective he lost a lot of his dps. Not only on the impact damage but also on the auto attacks that he now can't use because their is no slow. Whe have to take in mind that Smoke Screen is not designed as a close range withdraw tool and that the function from this ability both offensive as defensive really have a hugh gap unlike other abilities. Offcourse if you really want to give him a bit more ballanced burst they might could buff his midgame damage on it like:
- From: 60/110/160/210/260 (+60% Ability Power) magic damage on impact
- To: 60/120/180/240/300 (+55% Ability Power) magic damage on impact (for a more burstly mid game)
- OR To: 70/120/170/220/270 (+60% Ability Power) magic damage on impact (for a more burstly early game)
However, I won't see riot do this anytimes soon. Graves is just in a to strong position right now.
I think you miss the OP's point. The kit may make sense on a technical level, but the OP is pointing out that thematically, AA reliance and attack speed steroids do not support the idea of Graves wielding a shotgun.
If you are unaware, a shotgun is a slow, excessively powerful weapon that fires a round that essentially explodes into shrapnel or it fires a large metal slug that can put a hole through a wall with ease. It can only hold about 2-10 shots depending on what kind of shotgun it is, with manual holding the least, and automatic holding the most. The closer the target is to the gun barrel, the more lethal the weapon becomes. There is practically no way at all to increase how fast you fire the weapon past a certain point, so the attack speed steroid and an AA based play style are contradictory to what a shotgun is.
To make it fit thematically, Graves should be a caster style ADC, with spells and abilities that give him spray and higher damage the closer he is to his foes. He should have slow, but immemsly powerful AA, and maybe even a passive somewhere in his kit that makes his attacks hit multiple targets. Then his kit would make sense thematically and be a little less cookie cutter.
. I mean, come on... why doesn't her Q provide a shield, block the next incoming spell and restore mana on 50% critical chance?
will NEVER see any competitive play due to his inherent unreliability. But look at him now, a top-class lane-bully.
was reworked. As one of the few people who mained him pre-rework, he was perfectly capable of holding his own. But there was no denying he was poorly-designed, and Riot fixed him.