Public or private ate, costs could be cut. Unfortunately governments tend not to be great at running businesses.
Regarding your Dutch example, how does splitting them into the constituent parts you mention make things better?
The point is the idea about the private market is that the consumer punishes companies that are merely there to make money and therefore supply bad value for money. at least that has always been the idea. With something like water that's already out of the window, because you can't say ''this water company really really sucks, i switch to a other one.''
With vendor lock-ins and stuff it's also more difficult in other markets but that's an other topic.
The big difference in the dutch example is that the goverment funded and run(technically not run but owned by the goverment, local goverments to be precise, there are multiple of these companies each covering their own part of the country. ) water company is an not for profit company that does exactly what it needs, has all salaries capped and if it has millions to pay to it's non-existent shareholders it goes back to the goverment.
With waste water they went the same route as here in the uk and has also lead to raw sewege dumping, millions of money wasted and high bills., and shareholders getting an pay-out.