RFC 6979 - Why not simply hash the message & the private key for deterministic ECDSA? Why go through the trouble of using the HMAC_DRBG process, instead of simply hashing [message | private key] to calculate $k$ for deterministic ECDSA?

If the resulting $k$ or the signature is invalid, then a known byte value can be appended to the input, and re-hashed, until an acceptable result is achieved:
k=h([message|privateKey|0x00 … 0x00])

As many 0x00 bytes as the number of iterations it takes.

Am I missing an inherent weakness here?

Edit: If the hash function output length is smaller than the curve order, multiple hash outputs (produced by appending a known byte, similar to what was described above) can be concatenated as necessary:
k=[ h([message|privateKey]) | h([message|privateKey|0x00]) ... ]
Once you have enough output, you can then truncate it to match the curve order bit length.

And if the resulting $k$ or the signature is no good, then restart with the known byte appended:
k=[ h([message|privateKey|0x00]) | h([message|privateKey|0x00 0x00]) ... ]

And so on, until an acceptable $k$ is produced.
Deterministic signatures are safe in the random oracle model. Using HMAC_DRBG allowed me to rely on existing research on the safety of that construction and how close it comes to a "true" random oracle. If I had used any other "handmade" construction, then I would have had to provide extensive analysis on why it is secure. Being naturally lazy, I chose HMAC_DRBG.

Moreover, this use of HMAC_DRBG makes the end result more "convincing" -- and a large part of specifying a cryptographic algorithm as a RFC is to get other people to use it.

(If I had been aware of its existence at that time, I might have considered HKDF instead of HMAC_DRBG, but that does not matter much in practice.)