That is actually how Cassidy works in Overwatch - the tradeoff is the exceptionally small hit radius of the projectiles. But there are other games where your ability to hit buttons quickly matters. Fighting games, for example. The recent kerfuffle around Razer's snaptap keyboard (and the software version with "Null binds") have well demonstrated that technological advantages in the controllers bring advantages into the games as well.
On the flip side, I've played games which ignored the "fire" input for N milliseconds after triggering. Works well to prevent the issues mentioned, but was highly annoying as I would frequently click just a millisecond or so too early, and miss the shot.