Our Constitution was set up so that the federal gov't wouldn't gain too much power over the individual states (that part's fucked now) and that no single branch would gain too much power over the other two.
F'rinstance, if the Constitution were followed, the President is the overall supreme commander of the military, but he can't declare war. Only congress (Senate and House of Representatives) can do that. Also, the President can call for any program he wants, but the House of Representatives holds the purse strings, and decides how much of the budget will be spent on the various programs.
When there's a disagreement, the Supreme Court is to interpret the law & decide who is right or even if the law follows the constitution at all.
Even the hiring is not decided by the same people. The President is elected by an electoral college manned by reps of each state. The House of Representatives are chosen by popular election. The Senators were originally chosen by their state's legislature, but that's changed to popular election, too. The Supreme Court is nominated by the President, with approval from the Senate.
It's designed to be complicated and cumbersome because the Founders knew that so much power in the hands of mere humans is too much to resist and stay honest.