“Big Tech” already has a way to thwart them. reCAPTCHA, which bills itself as protection against hackers, indiscriminately denies service to users of anonymous browsers in order to force them to use something that makes them individually identifiable and trackable.
As a webmaster I encountered this problem with Google reCAPTCHA v3. I had to get rid of it on my commercial websites so privacy-based web browers like Brave could continue work.
I only care about password-guessing bots, so it was easy for me to develop a workaround.
I won’t use reCaptcha on any of my sites either. I use a honey pot and simple math question type captcha.