It's more that you can install "extensions" just fine, but need to be logged in to get "web apps". In reality, both are Chrome ran code, but there's the distinction there. You can however install basic extensions like adblock or ghostery without logging into Chrome.

(It won't help you on the anonymity standpoint of course, because every Chrome has unique id that's recorded when you log into any google service)

It's the "we require login to access any google docs documents if you use chrome, but don't need it if you use other browser" that's more annoying than web apps in my opinions.

Yes, some extensions use identity API's.