Sorry, but NameID does both, you're repeating work. You can log in using NameID to prove you own the Namecoin address linked to your Namecoin ID information. That's how it has worked for a while.
You're right but there's an important difference between NameId and BitID:
- NameID relies on OpenID which is a nice system but requires a third-party (the identity provider) to let you authenticate.
- With BitID, no third-party is required. It's just your wallet and the website.
Both systems have their strengths and their weaknesses. It's a matter of choice.