Actually it isn't. Congress sets the number of justices on the Supreme Court and the Senate must confirm all judicial nominations serving as an important independent check on the executive.
The Constitution basically gives the Chief Executive the powers that the people, through their elected representatives, will grant him.
You might want to read the document and notes and comments made by the Framers on the same. The powers of the Chief Executive are outlined in Article II of the Constitution. His powers are the creation of the Constitution which is the supreme law of the land and he can't revoke any of its provisions even if Congress so decides because Congress doesn't have the power to legislatively overturn the Constitution (see Marbury v. Madison). The Constitution can be amended but the President literally has no role in the process.
Enemy combatants, IMHO, should be held for the duration of hostilities. US citizens in Padilla's situation ought to be handled on a case by case basis, as they are now.
Given that the "hostilities" are never-ending, you're effectively holding these people for life. And I'm uncomfortable with giving the President unilateral power to deprive someone of their rights.
choose, currently, to trust the Administration's actions and judgment in this case for reasons stated in my previous post to you.
And what is your basis for this trust? What if the President is lying about the evidence or that the evidence was miscollected? These are also possibilities and good reason why independent oversight is needed.
those combatants can receive due process - through military tribunal - no one is arguing that Padilla should be held forever without due process.
the courts on the other hand - are even looking to extend these rights to NON-CITIZENS. Should Khallid Sheik Mohammed have any rights in the US civilian court system?