The current situation may qualify as a situation where "public safety may require" that the writ be suspended.
Article 1, section9, clause 2, US Constitution--The Privilege of the Writ of Habeas Corpus shall not be suspended, unless when in Cases of Rebellion or Invasion the public Safety may require it.I don't necessarily disagree with your premise. However, Article 1 deals with the powers of the Congress. Congress hasn't acted on any legislation to suspend habeus corpus. The Executive has unilaterally decided to hold people indefinitely. Find something in Article 2 that allows the executive to suspend habeus corpus without any action by the Congress.The current situation may qualify as a situation where "public safety may require" that the writ be suspended.
The problem is inaction by the Congress to make these things completely legal. Congress hasn't declared war, though there's no denying that we're in a war. Congress hasn't acted to suspend habeus corpus, though there might be a pressing need where "public safety may require it.".
In short, Congress is not doing its job, mostly for political reasons. Because of this, the executive is overstepping it's authority and making law by declaration (executive orders). Then, the minority in the Congress complains about this.
Bring a declaration of war to a vote in the House and the Senate. Bring a bill authorizing the military tribunals to a vote in the House and Senate. Let the votes fall where they may, and let the executive execute and enforce the laws as written, not make up new laws as they go along.