That is a good idea! At present, the effects of public sector and military support are determined by the percentage figure you attribute - regardless of how much money that is. That means a good tactic is, on years when the budget is very low, to put a large percentage into either the public sector or military support.
Essentially, the higher the public sector percentage, the lower the chance of a riot. Also, the higher the military percentage, the lower the damage caused and hence, the lower the loss to your next budget.
Changing the whole system so that you need to build (and maintain) specific public sector or military buildings is a large change but should be quite easy to set up. The hard part would be finding the small snippets of code that rely on the current system. They would still work regardless (you still assign a percentage each year) but would render any changes to just cosmetic.
It's definitely a good idea and would improve the game. However it would take a long time to change, taking time away from other areas.
I think I see this as a future change in an update after the game is released... Although it depends on how much support the idea gets. Who else thinks this is a major issue?