Yes, they most likely do have something to do with it. If Google is unable to ID you in some way (e.g. browser fingerprint, cookies, IP, etc) and determine you're a good Internet citizen, they'll assume that you could be a bot and offer challenging Captchas. It's annoying, but on the bright side it proves that your privacy add-ons are working!

Same here. When this highly advertized service was launched ('just a click!') it worked perfectly. Slowly, over the past couple of years, they deliberately replaced that wonderful service with another one where we act as Google's unpaid workers.