Circumvesuviana

Because southern Italy has been systematically starved of government funds for dozens of years. Why are there potholes in Chicago? Because citizens are unwilling or unable to pay enough taxes to properly fund infrastructure. Politicians do not have will to levy taxes for traditionally provided government services. You might well ask why you have to buy CV ticktets from a newsstand instead of a human booth. In the U.S. that is called Reducing Headcount or Outsourcing. Welcome to the third world, right in the USA!

Edit: Thanks to Cathy for explaining that there are virtually NO staffed ticket booths in the Circumvesuviana, except at the main Naples rail station.

FYI: If you were to take the bus to Tivoli (a suburb of Rome), from the big bus station at the Ponte Mammolo Metro station, you would find (after going upstairs to the completely unattended bus station) that you have to go back downstairs to the newsstand to buy your bus ticket towards Villa d'Este or Hadrian's Villa. It's not just Southern Italy.

But is it privately owned?

It is not privately owned. It is run by a government agency.

We were able to buy tickets in Sorrento from a staffed window in train station.

The OP wants to know why there are no ticket machines, like in many Trenitalia stations.
Jazz, did you mean that just the St Agnello station is lacking machines, or that one AND Napoli Garibaldi as well?

(Editing to add: I seem to remember that neither Pompeii Scavi or Sorrento stations had machines: bought our tickets from a human).

I am not sure what the difference is: machine or human ticket seller.

While not directly addressing the OP's original question, this string has sparked some interesting responses. Pure conjecture on my part, but could the lack of automation/machines in that region be because they might be seen as a threat to traditional service jobs for live people (like ticket sellers/cashiers)?

Why are there potholes in Chicago? Because citizens are unwilling or unable to pay enough taxes to properly fund infrastructure.

Well, considering the fact that one political machine has been controlling what "properly funding infrastructure" means in the city of Chicago for the past 70+ years, not sure the blame for potholes lies with the ordinary citizen. Unless, of course, it's their fault that they keep electing the same folks over and over who never do what it takes to actually fix the potholes. : )

I am not sure what the difference is: machine or human ticket seller.

You may not have to stand in a long ass queue like I did if there are machines

Ah. Figured queues at the ticket window may have been the reason for the question.

Not that this is an answer but a little digging around turns up reports that tickets may also be purchased at some nearby newsstands and tabacchi.