Government influence is what inflated healthcare costs in the first place by removing all aspects from true consumer choice (aka - the market).
What other product that people need can people not buy no matter how much money they have?
Courts/police are relatively straightforward and cheap, and act as an enabler for contracts and personal choice.
Of course, many more people spread colds, cause accidents, etc than commit crimes, so it makes sense that the cost of controlling their externalities is more than those of criminals.
But your choice seems arbitrary: you couch it in pragmatic terms, because you're not categorically against government programs, but then avoid actual cost-benefit analysis, rendering your opinion nothing more than whim.
That's what it always seems to come down to with "libertarians": unprincipled bullshit that aligns with their whims (such as yes police, no NHS).
Healthcare doesn't stop people from spreading colds. You're not actually reducing externalities with most categories of care. And if there were no police you would see a lot more theft.
Anyway, you can put it in cost-benefit terms, but you have to include a strong freedom factor. A government that takes 2% of GDP to keep public order is far better than not doing that. But taking a very large fraction of income to provide health care? That is an enormous cost to both spending and freedom, and reasonable people can see those costs as higher or lower than the benefits.
If it includes vaccinations then yes, it very much does.
If not, why not? Do the same reasons not apply to healthcare?