I get what you're saying, only in some sectors, public services deliver can deliver services according to need, for example I work in a state school, and we meet the learning needs of students extremely well and make real value added improvements to their learning. We are part of a centrally planned department, yet individual teachers are able to match their styles to the needs of learners. If one wants to talk in terms of 'products' then, if state sectors can produce, say a learning 'product', then why not other products?
Because the state has advantages in the production of what we call public goods, but has disadvantages when it comes to the production of private goods.
Public goods are commonly thought of as transportation systems, education, national defense, law enforcement (and in Europe, healthcare).
In economics, a public good is a good that is non-rival and non-excludable. This means that consumption of the good by one individual does not reduce the amount of the good available for consumption by others; and no one can be effectively excluded from using that good
For example, if one individual eats a cake, there is no cake left for anyone else, and it is possible to exclude others from consuming the cake; it is a rival and excludable good, or a private good. Conversely, breathing air does not significantly reduce the amount of air available to others, nor can people be effectively excluded from using the air. This makes it a public good. These are highly theoretical definitions: in the real world there may be no such thing as an absolutely non-rival or non-excludable good; but economists think that some goods in the real world approximate closely enough for these concepts to be meaningful.
Public goods provide a very important example of market failure, in which market-like behavior of individual gain-seeking does not produce efficient results. The production of public goods results in positive externalities which are not remunerated.
Because no private organization can reap all the benefits of a public good which they have produced, there will be insufficient incentives to produce it voluntarily. Consumers can take advantage of public goods without contributing sufficiently to their creation. This is called the free rider problem, or occasionally, the "easy rider problem" (because consumer's contributions will be small but non-zero).
(that's from wiki, but its a good article. I helped edit it).
(remember, goods is a catch all term and may not refer to tangible goods)
The debate then when it comes to central planning or say government production is what goods a centralized authority is better able to provide than the market. I would say that there is never an actual cut and dry, black and white, yes or no answer for almost all good types. It will depend on the style of economy and its peoples institutions, beliefs, and culture, along with its technological and/or educational level. Education is a good example of this grey area. In the US version, public and private schools compete for students and funds at the secondary level, but primary education is primarily served through local governments. However, the adoption of magnet and charter schools in many inner cities has occured where the government has been unable to provide an adequate product (and most of these moreso free-market solutions appear to work in the areas they have been adopted). This had led to a mix-mash of public and private sector involvement in education.
A government would probably do better determining how many soliders a country needs for protection than the private sector (costs would be unbearly high on each person, and there would be incentive to forgo protection). However, the private sector would do a better job of knowing how many boxes of Lucky Charms the country will consume in a given period.
If we look at public vs. private goods, we can see where our political debates wind up occuring, and what may work and may not work when produced publicly or privately.
The current solution to the problem in the developed world is that one runs a relatively free market but there is significant government involvement. The government can afford to be involved in the production of many goods that wouldn't otherwise be produced because of the increased wealth of its citizens over time.
I mainly ignore the third world here because most of the governments can be classified as predatory. Since their countries have yet to adopt or have sufficient experience with the instiutions of democracy, governments tend to extract resources and live the high life (whilst most of its people starve) until another bloody revolution occurs.
