Problem is that in the public sector (and I worked in it for many years) you get a layer of front line workers who are keen to do their job, enthusiastic, and wanting to give a good service, smothered by layers of incompetent managers who just want a quiet life and to advance their careers. Career advancement can be achieved by brown nosing and joining the right clubs. On top of that structure is a layer of political and administrative control by people with their own agendas but who know very little about whatever it is the organisation does, and the whole is permeated by a whiff of corruption.
To make matters even worse, public sector organisations have a sprinkling of mad geniuses who get an idea into their heads and push it through, with nobody able to stop the bandwagon.
At the same time, because the brain dead layer of middle management rarely leaves their desks, problems obvious to front line workers and the public who use the service are not picked up and dealt with.
Leaked profits are a price worth paying. Watch how Great British Rail performs. They can't even get a basic functional livery on their trains.
The real problem with the private sector is the emergence of oligopolies, largely due to political measures such as EU competition rules which have squeezed out the smaller players and given us the worst of all worlds.
Small independent public sector bodies with devolved local control and financing seem - at times - to give good results and value for money. But railways the world over are a black hole for money.