This is so right. We training Whisper Large model on 20,000 audio samples specific to a domain and it ended up reducing the ASR by 5% while improving WER of the finetuned domain by 0.5%.
Instead we ended up with no finetuning. We give audio snippet to 2 AsR models, take 3 best transcriptions and ask the LLm to pick the best based on the context. That produced significantly higher accuracy in how an agent understands the users.