I agree that for most web app this will be an extra formality. For me personally the key point is that there will be web apps that Google does not agree with from a business POV. That is my real problem with this.
If this list was curated by a community rather that Google, I would not have a problem with it.
It's certainly worth acknowledging that even if users aren't truly blocked, they may be turned away from legitimate apps that just haven't gone through the review process yet -- too many extra clicks, concerns about the legitimacy of the app, whatever.
I wonder how this in particular differs from the vetting process for any mobile app store (Apple's App Store in particular comes to mind with its reputation as a walled garden [1], but Android does also warn the user when enabling the installation of third-party apps not on the Play Store).
[0] http://www.pcworld.com/article/3194816/security/google-docs-...
[1] https://en.wikipedia.org/wiki/IOS_app_approvals
Disclaimer: while I work at Google, I have nothing to do with OAuth or any other user-facing interface.
Perhaps it should have a "tell me when they're verified then" option.
For apps that aren't vetted you have to confirm that you really intended to give them access. This is good! It protects most users who aren't a genius like yourself.
Even if you're not verified, users can still grant your app access! Nothing is blocked! Google just wants to be sure the user realizes what is going on.
Again, this is NOT about Android or Chrome apps. So yeah, go use whatever apps you want, as long as it doesn't want the users to grant the developer permission to do stuff with the user's Google account, this does not affect you in the slightest.