There will obviously be more applicants than positions in such a ministry, so what will the criteria for selecting people be? Whoever has the best academic qualifications? And who makes that selection, and who selects those making the selection?
In addition, are you arguing that people merely be given positions in government because of their 'education'? Education does not mean someone is a good administrator or free of flaws and corruption.
A government is theoretically (In my book) designed to govern the people in a nation in the most equitable manner possible and create conditions for economic prosperity and growth. The best judge of a government's performance are therefore those that government is designed to serve - the people of a nation, since they are the ones most affected by the actions of government.
So the need is for educating people of their rights and responsibilities with respect to electing their representatives, so they can make informed decisions, and not to take away their right to elect their government, and merely have it imposed upon them by a council or coterie that might very well be power hungry and corrupt, and has no checks or balances on it.