In a private healthcare system, where the government doesn't directly pay for its own citizens' healthcare issues, the government also lacks an incentive to keep its population healthy - which can go from allowing food companies to put as much sugar as they want not just in sweets, but in meat, sauces, and so on, to allowing companies to pollute the air as much as they want.
In a private healthcare system the insurers are also incentivized to pay for as few treatments as possible, hospitals are incentivized to make patients pay as much as possible for all the tests or unnecessary surgeries they make them have, and Big Pharma, as you said, is incentivized to make drugs that don't actually cure people and to price the drugs based on "value provided to the citizen". So if it's something like cancer, the value is a lot, even if the drug costs little to make.
In a private healthcare system the insurers are also incentivized to pay for as few treatments as possible, hospitals are incentivized to make patients pay as much as possible for all the tests or unnecessary surgeries they make them have, and Big Pharma, as you said, is incentivized to make drugs that don't actually cure people and to price the drugs based on "value provided to the citizen". So if it's something like cancer, the value is a lot, even if the drug costs little to make.