These things that you wrote about are very true and real. It's as if the health workers are doing way lesser work because the cost of treatment is also less.
But another side of the story is that some of these doctors and nurses in the government hospitals are not well paid and not considered important. Some of these doctors have connection with private hospitals where they earn better money. The ones without good connection renain just in the government owned hospitals and many of them become less passionate, caring, etc because they are not paid well.
Some other government owned hospitals are not receiving the full support they need to have well-trained health workers, adequate and fastest equipment and facilities. I've been to a government owned hospital and after prescription of drugs, I was told to go get from any other pharmacy because they are out of drugs. ( rumour has it that the ones in charge of the drugs sold to private hospitals to make more profit)
There are some issues where the government is not the only one at fault, the people also might be the problem.