I use Firefox and Firefox Mobile on the desktop and Android respectively, Chromium with Bromite patches on Android, and infrequently Brave on the desktop to get to sites that only work properly with Chromium (more and more often - another whole separate can of worms too, this...) And I always pay attention to disable google.com and gstatic.com in NoScript and uBlock Origin whenever possible.
I noticed something quite striking: when I hit sites that use those hateful captchas from Google - aka "reCAPTCHA" that I know are from Google because they force me to temporarily reenable google.com and gstatic.com - statistically, Google quite consistently marks the captcha as passed with the green checkmark without even asking me to identify fire hydrants or bicycles once, or perhaps once but the test passes even if I purposedly don't select certain images, and almost never serves me those especially heinous "rolling captchas" that keep coming up with more and more images to identify or not as you click on them until it apparently has annoyed you enough and lets you through.
When I use Firefox however, the captchas never pass without at least one test, sometimes several in a row, and very often rolling captchas. And if I purposedly don't select certain images for the sake of experimentation, the captchas keep on coming and coming and coming forever - and if I keep doing it long enough, they plain never stop and the site become impossible to access.
Only with Firefox. Never with Chromium-based browsers.
I've been experimenting with this informally for months now and it's quite clear to me that Google has a dark pattern in place with its reCAPTCHA system to make Chrome and Chromium-based browsers the path of least resistance.
It's really disgusting...
I read that the "level of annoyance" (phrasing mine) has to do with your score (i.e. how likely Google thinks you are a bot). And I wouldn't be surprised if using any browser other than ones in their ecosystem reduces your score more.
Anyway, there are other captcha systems websites could use but choose not to.
You hit the nail on the head: Google has made itself the de-facto default for many web services, so that it takes extra effort to go with a privacy-friendly alternative. That's what makes Google so dangerous: it's their customers who make them unavoidable, be it for reCAPTCHA, fonts, basic Javascript, login, analytics, maps... the list is endless.