Many have asked this question you ask and it has always puzzled me. Let me ask you to carefully review your statement that I referenced above.
The crux of the question usually comes down to why should terrorist have access to the rights granted others by the Constitution.
The label "terrorist" is where my puzzle begins. Substituting other words for the word terrorist doesn’t solve the puzzle.
Why should terrorist thieves have access to the rights granted others by the Constitution?
Why should terrorist murderers have access to the rights granted others by the Constitution?
Why should terrorist kidnappers have access to the rights granted others by the Constitution?
Why should terrorist rapists have access to the rights granted others by the Constitution?
Why should terrorist have access to the rights granted others by the Constitution?
These questions have merit in my opinion and clear thinking will provide the answers. Mankind struggled for thousands of years to achieve due process in law. I would think that the only way man would give up due process is be dragged kicking and screaming away from it. It is wise to recall that the Constitution does not, in fact cannot, guarantee justice; the Constitution does however grant all of us due process in law. Before we allow due process to slip away, it would seem fair to examine the intended and possible unintended consequences of such a drastic action.
My observation is simple. Actually, my observation is a question which when answered provides the reason why terrorist must be granted due process. My question is; how do you know who is a terrorist? How do you know who is a terrorist, thief, murderer, kidnapper, or a rapists. The way you know is by allowing them due process.