Dr David Unwin has repeatedly mentioned how those of his T2 patients who go low carb saved his surgery approx £40,000 in the first year. The money saved was from the budget used to pay for patient medications.
So yes, surgeries (and the NHS as a whole) could see huge benefits and savings from actively supporting low carb, where appropriate, for patients.
The difficulty would be finding surgery staff (docs and nurses) willing to educate and embrace the idea of low carb. This would take a lot more investment of time, and effort than blindly following orthodox medical advice. It is a big transition to become convinced of the benefits of LC, then find out how to use it effectively (food, nutrition, pitfalls, cholesterol, etc.), then get other staff on board, then bring them up to speed, then create systems within the practice to support both patients and staff, then convince the patients of the benefits, and then support them until they get the hang of DIY LC. Not everyone wants to change, is computer literate, and is willing to self educate and self implement.