There are two things. One is that something things it doesn't make sense to have multiple companies offering multiple versions. Specifically, right in front of my house, there's no place for a dozen companies to put multiple roads for me to get to work on. it's a highly un-free market because of physical limitations. For those, a simplistic model makes sense. Everyone contributes to a pot which is used to pay for maintenance because everyone benefits. Other things, it makes sense because the indirect nature of its benefits means the short sighted will opt out of. Eg elementary schools for children. If you don't have, and don't plan on ever having kids, you'd opt out of paying for that, but it's in your best interests not to have an uneducated population for a lot of reasons. Or take hospitals. As a young healthy person who's never needed to go to the hospital, you'd opt out of paying for them, only to have problems when you do get old and need to go to one. Hell, if I don't drive and don't have a car, I'd shortsightedly opt out of paying for road maintenance or the DMV, only to realize that I rely on that. Same for a vast number of other services that you don't see or need every day. How often do you think about the supply chain that supports the water treatment plant when you flush the toilet?
It's an interesting thought experiment, but it fundamentally misunderstands the reason for government to exist, which is not to turn a profit.