Onename is a registrar app that runs on Blockstack. It is one of several ways to register names.
If we used OAuth in the manner you described, users and app developers would have to trust the Onename website. This is how centralized systems like log in with Facebook or Google work. By trusting a third party (how OAuth works), the third party can impersonate users, prevent them from logging in, collect information or track the users' usage of your app, etc. It also introduces a single point of failure.
With Blockstack running as client-side software on the user's computer, we remove that element of trust. A user can log into your app. You, as the app developer, don't have to trust any one.