Caitlyn - Why does her passive scale with Attack Speed?

It was nice when Caitlyn's update gave her automatic headshots against trapped and netted targets. That made sense, it worked with the kit, and it's fun. But they kept the old attack-speed scaling part, where she gets a headshot after every X attacks. That makes no sense for a sniper character. With Jhin revealed, and a lot of other marksmen with long range snipes, Caitlyn's identity as THE sniper seems to be in danger.

What would be the pros and cons of switching her headshots so that rather than occurring after a certain number of attacks, they occur when one of the following criteria is met?

1. She has gone a certain amount of time since her last auto attack. This is akin to Ashe's old passive, but it makes sense for Cait's concept. Time in bush could count twice. For example, after 4 seconds of not attacking, her next attack is a Headshot.
2. When an opponent is reduced to a certain percentage of health, her next attack against them is a Headshot. This might necessitate a bit of a nerf, but it reinforces the feel of the "headshot" finishing blow.
3. Her attacks have a flat % chance to Headshot opponents, possibly scaling with slows, snares, and other movement impeding CC. It's a little wonky with Crit Chance, providing a second randomized effect, but perhaps Crit and Headshot could be synonymous, or Headshot could be removed in favor of "guaranteed crits under certain conditions".

Again, all of these ideas are intended to be included WITH her passive's new "Headshots vs trapped and netted enemies" bit.