Most companies only care about how much insurance they have to pay and their bottom line they have no reason to keep an eye on the big picture.
If an employee gets sick for too long or dies they will just fire him/her and get someone else to replace them.
The citizens health is a big picture thing that only a government has the incentive of maintaining.
What is that incentive, and how is it stronger than the incentive to create jobs or lower prices right now for people who vote today by allowing some environment-destroying industry to expand, said expansion being the cause of future illness (a hypothetical or maybe not entirely hypothetical example)?
Those people are and will be paying the pensions of the current voting population.
QED.
If a Government needs to spend $100k in tax payer money to save somebody's life and this somebody pays back $200k in taxes, this is good business, isn't it?
"The government" (why the capital G?..) as an organization might have an incentive to protect taxpayers' health but individual people making up said government do not have the same incentive. I think they call it the agency problem.
(Some people go as far as advocating benevolent dictators with a hereditary right to rule; of course in reality few dictators are benevolent, and a hereditary right to rule prompts people to kill off ruling families. I conclude that setting up incentives such that everything works out smoothly is rather damned hard.)
That's definitely a problem. Problem with democracy though and not capitalism. The policies are designed to have 4 year lifespan because elections are held every 4 years. Actually, it is quite a big flow when you think about it. Politicians are not only incentivized to look short-term at their policies but also to design them in the way where long term negative effects are desirable if one can be sure that the opposition party will take over after next elections.
That's why Western democracies are watching places like China carefully where you can design long-term policy and still benefit from capitalism. I believe that the main reason behind the US to introduce more and more authoritarian policies (i.e. militarization of police force) is because they see that it works well for China. I mean marrying soft authoritarian form of government (like in China) with capitalism might be superior (economically and socially more effective) compared to having liberal democracy combined with capitalism.
The collective principle asserts that... no society can legitimately call itself civilised if a sick person is denied medical aid because of lack of means.
I think it is worth noting that the book by Aneurin Bevan, the founder of the NHS, from which that quote comes was called "In place of fear" - that's what we had before socialized medicine (NB not claiming that the NHS is perfect, it clearly isn't - but compared to a lot of the alternatives it's fantastic).
Of course, we do deny some care because the NHS can't pay for every treatment for everyone - but at least they try to decide this in a fairly sensible evidence based manner.