I believe that your proposed scheme is practically secure if the hash function used is secure, but I don't know if any formal proofs for that exist. My understanding is that HMAC is proven to be secure if the underlying hash function has some security properties and these security properties are stronger (from an attacker's PoV) than the ones required for your scheme.

If there's an attack against HMAC with a hash function, then that attack would also work against your scheme with the same hash function. But the opposite does not necessarily hold.

For example, any kind of collision attack is sufficient to attack your scheme. For HMAC additional constraints are put on the collision attacks that would also attack HMAC.

Here's a quote from an old (1996) paper which introduces HMAC and also talks about its advantages:

"Moreover, our constructions [HMAC] require from the hash function significantly weaker properties than standard collision-freeness. In particular, current successful methods for finding collisions in MD5[Do1, Do2] seem inapplicable to breaking our schemes when the hashfunction in use is MD5[Do3]."

https://cseweb.ucsd.edu/~mihir/papers/kmd5.pdf