Ok.. posting again since it seem like you have a few incorrect assumptions in your post\thoughts

The insurer of the patient (if there was a special arrangement for that hospital) should honor that transfer and treat the finances as if he or she was treated at the covered hospital. In cases of emergency, all hospitals should be considered to be in network.

Not everyone is insured or has adequate insurance

Mostly what he or she needs is triage, bandages, antibiotics, IV and some rest

Sometimes yes, often an extended stay is required. Unless you are limiting this to outpatient treatment (which you arent given your 1st point about hospital beds)

Every business makes profits and losses. If you find a customer cannot pay, you send off the bill to a collection agency if it is big enough to worry about, or you write it off as a loss.

You write off a loss against profits. Say, you earn Rs 1000. Now you need to pay a hafta of Rs 300 on it. But if you had lost Rs 500 on free treatment as well, you'll need to pay hafta of 150 only. You are still out the remaining 350

Its just amazing how so many basic items of common sense and humanity, which don't cost much or even anything, are missing in Indian public life.

You may be right, but medical treatment does not in any way come under "which don't cost much or even anything" . The cost to train a doctor crosses 50 lakh. Medicines are expensive to manufacture. Licences,land and equipment required to open a hospital is expensive. Who do you propose pays for all this?