If I’m understanding your points correctly here, you’re accepting the idea that disease control is a valid concern. And you’re accepting the idea that disease control is not a direct profit-making business. So it’s the equivalent of national defense - something that benefits everyone in general but nobody individually. So moderate libertarians accept that this is a legitimate cause for a government to tax its citizens and pay for a service.
My question is why does privatization step in? We’ve established that things like national defense and disease control have one customer - the government. So why not just have the government handle it directly? If the government is going to be collecting taxes and then paying that money to people like soldiers or medical researchers, why shouldn’t the government directly employ these people who are performing work exclusively for the government? Why “privatize” the service and insert an unneeded layer of corporate ownership between the people who are writing the ehcecks and the people who are doing the work?
Let’s say American disease control needs 10,000 doctors and medical researchers and managers who have a collective salary of $400,000,000 a year. The government could establish a National Disease Agency that employs those 10,000 employees and pays them the four hundred million. Or the government could hire some corporation to do the same job and just write them a check for the work. So the General Disease Corporation employs the 10,000 people and pays them four hundred million dollars. But the corporation also has to make a profit which the government does not. Let’s assume a modest annual profit of one percent. What exactly did we get for that extra $4,000,000 we spent? I can see what the owners of the corporation got - they got four million dollars. But what did you and I get as taxpayers?