They can. Right now each hospital or dispensary is run by some board or comittee. I dont think in any developed country we have this kind of situation. Hospital should be run by HMO or insurance or better yet universities. Something to free counties from managing drugs, nurses, doctors, etc.
If i was a governor - I would make each of those hospital - privately run or outsourced - and then use budget to get everyone NHIF cover. A county of 1 million people - have maybe 300K households - NHIF cover of 500 per month - 1.8B. That is about how much many spend on health budget and do a bad job at it.
Once everyone has NHIF cover - they can go to those former county hospital or private or missions. That 1.8B gone to NHIF will remove lots of headache running hospitals.
Just float a tender for someone to take up all county hospitals - run them - pay salaries - whatever - it doesnt matter - as long as each resident has NHIF. Many missions and churches will be happy to run those hospitals.
Can a county form an HMO? All the public hospitals from village dispensaries to level 4 hospitals to be run by one entity. The HMO would pay salaries purchase medicine, equipment etc Create its own health insurance for residents, accept other insurance and obviously cash. Run properly it'd draw patients from other counties and also from private hospitals. They can even have private wing in hospitals. Just wondering....