Why is this not a more common way for generating 12 words?
Probably because it's a lot of work, and not recommended because people will start cherry-picking words to form a sentence.
I intend to flip a coin 121 times, convert to BIP39 words and then enter them into my HW with a random 12th word until it accepts the mnemonic as valid (passing checksum). This way I'm not relying on the HW RNG.
Why stop flipping there, if you can keep flipping coins and find the nearest word that matches the checksum?