The Real Problem With Assassin's Dagger
Everybody's focusing on the perfect storm that allows the proc to get a killing blow in a 1v1. That's an extremely myopic point of view. This is the real issue:
It effectively amplifies the damage from everyone attacking the target. So on ganks, roams, and picks, it will be far more difficult to survive. For example, let's say Talon roams bot. He blows up the enemy ADC without an AA while Talon's ADC (let's say MF) and support are attacking the enemy support (let's say Leona). Talon has no more CDs to blow on Leona, so he starts AAing her for minimal damage. Meanwhile, MF channels her ulti for 2 seconds and the support Sona uses her Q power chord.
For the sake of simplicity, we'll use even hypothetical numbers to get to the point. Leona has 2000 hp. Talon only did 300 damage to her. MF did 900. Sona did 400. The total is 1600 damage but Leona takes 2000 damage. Talon's item effectively increased his own damage by 75, but it increased MF's damage by 225 and Sona's damage by 100.
Herein lies the problem. This item single-handedly gives AD champs support utility throughout the entire game regardless of scaling/falling off or whether they are fed or behind. Assassins are designed with an element of feast or famine - feed or get fed. ADCs are designed to farm and outscale. By design, mages and supports trade mobility for utility. And by design, most fighters can fall back on building tanky.
Assassins are designed to be mobile, have jukes, and get kills. You counter this by coordinating with your team to shut them down and prevent the snowball. The same applies in bot lane; shut down the enemy ADC so your team is the one to outscale. Building Assassin's Dagger skirts around this design philosophy by allowing AD champs to simply support any fed player on the team by effectively increasing their allies' burst by 25%.
Having played assassins, I know how frustrating it can be to play from behind, and every game I play as an ADC is playing from behind. Maybe this is a good design addition that just looks super unhealthy from the outside? If that's the case, why are we giving AD champs tools to play from behind while AP assassins are stuck being nearly useless if they can't snowball? Discuss.
TL;DR: Item gives AD champs utility to play from behind, which is bad on classes designed/balanced around snowball and scaling.