Empires like the Romans made some basic inroads into these problems (although in Rome, murder was still a personal matter, banditry was still the norm, etc). Building an aqueduct or a road is a massive quality-of-life achievement for everybody.
I think in general, for antique societies, they don't have detectives - if a crime is committed, the first problem is, there's no state agency interested in investigating the matter.
The claim that murder was a 'private matter' is from Emma Southon, but it makes a lot of sense to me. Pre-modern history is rife with blood feuds that are basically the 'private' way of preventing murder. The state typically wouldn't have the resources to get involved, even if they did have the interest.
If you imagine the chain of somebody_is_murdered to somebody_is_punished there are questions like: 'who reports the crime, and to whom?' and 'how do you establish the crime actually happened, in the way it was reported?' that are just really hard to answer unless you have a big state organization dedicated to managing stuff like that.
I suspect the differentiation they are drawing is that in "modern" society there are very few accepted reasons for killing someone, and all cases should be examined by an arms-length person.
This is very much not true across societies, or historically.
In the Ancient world, I don't expect murder of slaves or subsistence farmers would have any involvement outside of their families/owners/patrons.
It's fortunate that no action is required from the murder victim, I guess.
Did it have any advantage? Rome has a special place for Europeans because it's "our" ancient empire, but that doesn't necessarily mean it was superior all of its peers. Also, maybe those peer empires didn't build aqueducts, but they built different but equivalent projects instead.
But you can't get more slaves if you don't have more lands, but more lands means administration difficulty increases, which means you need more soldiers and bureaucrats, who are not directly producing food.
Rome was in fact special.
But to me it feels orthogonal to the benefits of increased state capacity, trade, and standardized coinage that helped provide the Roman Empire it's economic benefits. Yes much was built by slaves, but other empires also had slaves. So what was the comparative advantage of Rome?