Expecting to compete with this with only a few forward passes through a 0.5T-scale LLM is almost too hopeful.
With 10 minutes and scikit-learn I can get pretty good test-set accuracy for length of stay based on pretty bare bones input (time of day, mode of arrival, age / sex, bigram / trigrams of chief complaint). Given access to vitals, labs, historical diagnoses, a provider's (and their colleagues') historical practices, and a little PyTorch / HF transformers I bet there would be some low hanging fruit for suggested diagnoses and quick pick orders. Could in some cases streamline getting to the same end result, in others possibly make recommendations to bring practice more in line with current recommendations or to prompt investigation into uncommon presentations or rare diseases.
And certainly would have some sharp edges and potential harm too. But based on HN reports of experiences with US medicine, seems like the potential upside may be worthwhile.
The hard part is demonstrating the value of such apps to provider organizations, and getting them to change their workflow. Clinicians are extremely busy and don't want to click more buttons unless it improves patient care (and they get paid for it).