A wise man once said, He who controls the kings treasure, controls the king.
As long as Money is accepted, there isnt much the Charedim can do, The money can be cut off. When you take somones money, there is always strings attached.
So if the draft (or national service) is refused, Aid will be cut off and a decision will need to be made either accept some sort of draft/national service or endure even more poverty than exists now even starvation