What stops the US military from hauling you off to Guantanamo and calling you an enemy combatant. Once there, without habeas rights, what do your friends and family do to get you back? Under your argument, without habeas rights you cannot file, anywhere, to prove you are a US citizen. Unfortunately habeas corpus is the right to the proceeding wherein you prove you are a US citizen. The habeas right comes first, not the right to prove citizenship, because without the habeas right there is no judicial forum in which to prove citizenship.
Be careful what you think you are giving up.