Frequently, when economics are discussed people falsely believe that everyone has the same underpinning moral evaluations or the same ideals or objectives to what a economic system should do. As economics is an interesting combination of mathematics, politics, history, morality and law it is no surprise that we come to such wildly different outcomes to what type of systems we propose in terms of the relation of the government in said system, in spite of the fact that we all probably have a very narrow idea of what type of society we would like to live in.
Very interesting experiment, however your categories are not abstract enough. I think in the most abstract terms the society should be organized such that the most well-being of all present (and suitably discounted) future members of the society is maximized. From this your categories are more or less all in the depends category since they are just means to archive a goal.
*) The system should provide encouragement for social mobility. Merit should determine people's ability to rise in society, not birthright or arbitrary class.
As long as an equal society is not possible, social mobility is the next best thing.
*) The system should provide price stability and combat inflation.
No, inflation reduces the risk of enterprising individuals. Therefore I think that some inflation is a good thing.
*) The system should provide for the best possible degree of personal freedom in economic terms, freedom from regulation and taxation
The system should first of all provide for the essential political freedoms. If economic freedom is compatible with these, then they are desirable.
*) The system should encourage and provide means for research and technological discovery
*) The system should levy taxes to promote the construction of worthwhile public assets (i.e. infrastructure)
If a taxless system can be proposed in which infrastructure (etc.) is still build, then the system should not levy taxes
*) The system should provide a 'safety net' against extreme poverty
*) The system should provide in protectionism of select industries
In general no. However there may be reasons for protectionism, for example the domestic food production should be assured.
*) The system should subsidize, pay for or otherwise encourage education
*) The system should levy a progressive income tax
From my other answers, this is a inevitable conclusion.
*) The system should levy a flat tax
Probably one can actually prove in utilitarianism that a flat tax is actually morally wrong.
*) The system should regulate the business in matters of public health or pollution
Yes, since these are examples were the common interest and the individual interest diverge.
*) The system should seek to disrupt monopolies and cartels
Usually yes, however there are natural monopolies in certain markets. Disrupting these will just see the rise of the next one.
*) The system should regulation licensed occupations
No, except when strictly necessary.
*) Trade should be unregulated/free between countries
Yes. The only exception I can think of at the moment would be food shortages during a famine.