> (a) move smoothly/naturally and (b) introduce random noise.
Moving naturally is not that easy to code. Otherwise Google would not be able to tell if you are a robot or not simply by analyzing how you click a checkbox.
Google can't. They use your history of online activity across their services to decide if you're a robot. If you click the checkbox the exact same way as usual, but do so in an incognito window without any established Google cookies, they require you to go through a captcha.
Off topic: but why the fuck does Google operate two different captchas? One that is useable, and for internal services one that is incredibly difficult top get right on the first 9 attemps
it's also hard to define "move naturally" - if you look for smoothness you'd get a ton of false positive. check this out https://streamable.com/swz3y - twitchiness is a byproduct of scouting for target in motions.
Moving naturally is not that easy to code. Otherwise Google would not be able to tell if you are a robot or not simply by analyzing how you click a checkbox.