Unless you are arguing the An-Cap thesis that these functions can be conducted by private entities. If you are, then congratulations: we're already living under your preferred system! It is just that for most territory, one company has seized monopolistic control of the territory, has called itself "the government", and no other companies have been formed to challenge it. Exceptions such as the West Bank where two companies are competing do exist.
From the `Impossibility of limiting the government` section of `What must be done`[1]
"Now, once the protection monopoly (government) is in place, a logic of its own is set in motion. Every monopolist takes advantage of his position. The price of protection will go up, and more importantly, the content of the law, that is the product quality, will be altered to the advantage of the monopolist and at the expense of others. Justice will be perverted, and the protector becomes increasingly an exploiter and an expropriator. More specifically, as the result of the territorial monopolization of protection, two tendencies are generated. First, a tendency towards the extensification of exploitation, and second, a tendency towards the intensification of exploitation."
(A world of purely voluntary contracts and no compulsory purchase would never have got past the development of the railway or telegraph, so the whole prospect is ludicrous)
https://mises.org/library/100-years-myths-about-standard-oil
Crony capitalism is not at all "capitalism". It is an beast created by the state, through military spending, stimulation, infrastructure or the means of social wellfare. The more "militaristic" or "social" a government becomes the more leaches appear.
100% capitalism isn't practical and is unfair (e.g, to the poor and sick). What is a fair way to divide costs for road usage: time of use, miles driven, emissions, cost of vehicle, ability to pay? It's not an easy answer, and many are practically unenforceable. Hence, tax.
And for the record: I'm generally capitalist by economic viewpoint.