Being able to quickly reject invalid sessions identifiers is a useful property in some cases and is normally done by authenticating stateful session tokens with a MAC using a global app key. This can be used for DoS protection if the cost of a database lookup is more than the cost of MAC, and the complexity is justified. It ensures that the random numbers a user is trying to present as their session token are the numbers generated by the server if the key is not leaked.
Because you're trying to bolt things on top of JWT, you're creating a worse version of that stateful authentication pattern:
1. You lost the statelessness of JWT by making database queries. Your claim that "you don't need to verify against user's secret immediately" is false, as you need to do that in all cases immediately after verifying the JWT signature to get the benefits of your system (token invalidation). Sure, you reject completely invalid tokens early, but you still need the statefulness to authenticate users properly (if your goal is to be able to invalidate tokens).
2. In your version, getting a read-only access to the user database (leaking per-user secrets) completely destroys token invalidation, and all your authentication now depends on one key. If, in addition to that, the JWT signing key leaks, user authentication is completely destroyed and can be bypassed by the attacker, who now can sign in as any user. (A common way to leak all this is by failing to properly secure backups).
Compared to a stateful session system with split-tokens, where the database stores tokenId => verifier, where verifier is Hash(randomToken), and user's token is id||randomToken, read-only access to the database doesn't let the attacker authenticate as any user. If the tokens that users presents are in the form of id||randomToken||HMAC(serverKey, id||randomToken) for early rejection as above, leaking serverKey still won't allow the attacker to authenticate as any user. The attacker needs write access.
> Is author's brain stateless -- my bad, I thought this was not reddit
I didn't realize that you were the author, I thought you were a reader who was misled by this blog post. Even better: you can go and edit it, removing "stateless" everywhere! It's fun to invent various protocols, but when someone points out the errors, surely you'd want to fix them -- no shame in making mistakes if you correct them.
Usually, when I think of a protocol, after writing down "Benefits" (as in your blog post), I write "Drawbacks" and then try to come up with downsides and compare it with existing protocols. I'd suggest you do the same.
PS. Find yourself in this picture: http://cryto.net/%7Ejoepie91/blog/2016/06/19/stop-using-jwt-...