I support the general idea but there are a few specifics I'd like to point out.

I agree with Cornfeed on the fact that Ministries should not be fixed. Instead it can be part of candidate campaigns. Sketched demonstration: ''I see an issue or something lacking in The Coalition - This is my general goal and agenda - These are policies which will help me achieve the agenda - For successful implementation of these policies, I see these Ministries as being desirable to have - This Ministry will be assigned for working on these specific policies''. However, I do believe that two Ministries MUST exist as fixed, given the game mechanics: Ministry of Defense and Ministry of Foreign Affairs.

As for appointment of specific Ministers, I believe that should be left after the election has concluded. It is up to the elected Prime Minister to appoint who they think would help them reach the goal. I believe that this would give a certain weight of responsibility to the Prime Minister.
On the topic of responsibility, I believe that the Prime Minister should be held accountable to the Assembly. Besides motioning a vote of no confidence (which is an extreme case), perhaps codifying an obligation of the Prime Minister (or his appointed subsidiary) to present ''briefings'' to the Assembly on a regular basis. These briefings would detail what has been done, what is being worked on and what is being planned within the Cabinet in the aims of reaching the agenda set out in the Prime Minister's campaign. As for Ministers, they are held accountable by the Prime Minister who has appointed them and as such he has the right to dismiss them from that position, providing they give out a statement detailing the reasons for doing so.

Setting the agenda in the campaign would make them more substantial and would provide a good set of standards which both the Assembly and the Prime Minister could judge that specific term by. If the agenda isn't met, the term is judged poorly. However, it also provides a discussion on why the agenda wasn't reached. If the reasons prove to be of systemic nature, it further incentivizes a natural development of The Coalition towards efficiency.