Why are the removal powers so incredibly important to the President?
I assume that you are asking about the President’s power to remove government officials from office if he (or someday she) so chooses. If so, this power is incredibly important for presidents because it allows them to have the people they want in important positions in the executive branch.
Presidents rely on the executive branch to carry out their agendas. They have overall plans, but they have to rely on the department heads to actually put those plans into action. A stubborn cabinet member could thwart a president’s desires by simply stalling when asked to put the president’s agenda in motion.
For this reason, it is very important for presidents to be able to remove these members of the executive branch. Presidents should not be stuck with people they do not trust having the power to carry out or to thwart their agendas. Presidents are the head of the executive branch. As such, they ought to have the power to determine who serves in important positions in that branch. If they lacked the power to remove such officials, they would be deprived of some of their power as chief executive.