I constantly miss my first shot even when I'm stood still and aiming perfectly on their head because the first bullet decides to randomly fly off.

In beta, there was a lot of complaints about running headshots, so Riot introduced a slight delay between stopping moving and being able to shoot accurately. It was a garbage bandaid fix to try and placate all the whiners who got shit on fair and square, but because they got counterstrafed one-tapped they think it's run and gun.

I think the player base has matured enough that we can go back to that crisp feeling counterstrafing without everyone whining about how they are running headshot.