I agree that anonymity is orthogonal to the purpose of captchas, but usually a captcha is only required when you don't have identity. This can be because you haven't established identity, or because the identity is in question, but also because the site does not want to require identity. In fact, outside of first time user sign ups, most captchas are used specifically to allow people to engage without needing an account. So in most cases you use a captcha because you want to allow anonymity.
There already exists several systems like you describe: login with your Google account, Facebook, Twitter. There are already several comment systems (Disqus for example) which make using these as simple as using a captcha for sites who don't care about anonymity. We don't need to integrate identity into captchas.