Actually back in the days of PSU's like HAL, ITI, BHEL .. etc. These schemes where there.
You could even go to private clinics. I mean you could go to a good private clinic, get yourself good healthcare and it would be paid for with your + company's contributions.
There were even hospitals that ran minimal payment schemes like MS Ramiah Hospital in Bangalore. Where the hospital trust would finance the difference of treatment after your bills. Sai Baba hospital is doing an awesome job, I know many poor people who got their cataract operation done for almost what they could pay. But as you know our country's population is too high for these patch work attempts to work.
The Government of India needs to seriously reflect on
a. Health care reforms.
b. Insurance, and ways of making it work.
c. Cut corruption in government hospitals and other areas.
d. Taxes on essential commodities like medicine and equipment.
By all means tax the alcohol,cigarettes and other luxury stuff, but taxing medicine and things that save people lives. Isn't quite justifiable.