It is also plausible that because google analytics runs on so many sites that they could do something shady like put you in a pester segment if they see you coming from duckduckgo to other sites frequently. It is not hard to imaging using Recaptcha as a nuisance against other search traffic providers.

I doubt that many people would make a connection between their search engine and seeing captchas on other sites. So limited gain for, if anything, many unnecessary complaints.

This is why I love container tabs in Firefox. I like putting all of the recaptcha stuff in one container so it can't snoop on my other stuff (I'm too lazy to look into what it's doing with cookies and whatnot).

But honestly, I wish it would just die.