Recaptcha tracks users / devices, not IPs. A VPN won't help, it'll only lower your score. At that point: not allowing them to track you just means you can't use large parts of the web.
"You don't want that GPS tracker installed into your skull? Well, we won't force you, of course, but public transportation, government services and most grocery stores can only be used by GPS-skull-people"
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.