I'm actually from (East) Germany, but I moved to Singapore exactly because of the advantages you mentioned. Putting my tax-money where my mouth is, so to speak. And I have to say I am happy with the value-for-tax-money I am getting here.
If the private sector in your country can't handle infrastructure, I think the role of government should be to clean up regulatory hurdles and barriers to entry, so that the private sector can handle this task.
Honest and competent civil servants are one of the rarest and most precious resource in any country. Affairs should be set up, so as to economize on their time and effort required.
Singapore ain't perfect. For example, our government has significant ownership in eg an airline and quite a few other businesses. But still, Singapore is one of the best run countries for a neoliberal.
> Business tends to work well when the value created is short-term and can be easily measured and captured by the entity creating that value. For example, a grocery store.
I agree. I agree even more: any organisation works best when feedback is immediate.
> Government tends to work well when the value created is long-term and diffuse, and doesn't have a single point of capture. For example, the road network which the grocery store relies on to get both its goods and its clients to the store.
I disagree. We know that governments work badly at the best of times. Why would anyone think they'll magically start working better when the outcomes are harder to measure?
You could try to make an argument that both governments and businesses work badly under these circumstances, but that for some reason governments are slightly less impacted?
I mean, it's theoretically possible. But seems unlikely?
In your specific scenario: toll roads work just fine. Alternatively, the shop can also choose to subsidise road tolls for their customers. Just like shops often offer free parking already, or other freebies.
(And yes, I also think that governments should not be in the business of issuing currency either. At least they shouldn't have a legal monopoly. See eg https://oll.libertyfund.org/title/white-the-theory-of-free-b...
This is a minority position these days, but one with a long intellectual heritage.)