Is it though? I'm somewhat lucky, because my government is generally technologically behind and loves literal paper trails, but yours isn't. Plenty of .gov sites use recaptcha. Sure, you can still visit those sites, it's just that, unless you pass a captcha test, they can't verify that you're actually a person (and not a Russian bot) and can't let you do certain things. If you want to use those government services, you need to allow Google to track you, or maybe they'll add a "sign in with Facebook" option so you have a choice.

With invisible captchas, you can't even sit down and solve a higher number of riddles to prove that you're really human and know what a fire hydrant looks like even though you look kinda strange. If Google doesn't believe that you are human, tough luck. Unless you have a personal connection or a solid Twitter following that an amplify your concerns, nobody at Google cares. Does your government care? It makes their life easier and normal citizens never really had problems with it.

DHL makes me solve a captcha to login and buy postage stamps. There probably are, or will be, public transportation companies that use recaptcha. It helps them to combat voter fraud (crime, abuse, election meddling, fake news, lots of things) if they know where (on the web, for now) you've been in the last 6 months.

You don't like the "implanting" part, because that's unrealistic? Just wait 20 years, and it may not be your head, but an RFID chip in your hand (yeah, those exist already). Until then, carry your gps tracker around and install their software on it, so it can collect data on your behavior to make sure that you're not a criminal.

It is not "wild speculative hyperbole" not to give the benefit of the doubt to companies that have repeatedly demonstrated that they are not entitled to the benefit of the doubt.