The answer to the basic question of whether good enough plans are available to make such a kit is - yes. The Coast Guard Historian's Office has quite a few accurate drawings of the Eagle, though they come from a variety of sources. A few builder's drawings of the Horst Wessel (the Eagle's original name) survived the war. In more recent times draftsmen hired by the Coast Guard have made measured drawings of her in conjunction with various refits and other projects - and I got hired to do an outboard profile/sail plan of her in her 1994 configuration. If I remember right, the materials I got from Washington included such things as working drawings of the boat davits on the quarterdeck - which were recycled from a Treasury-class cutter that was being decommissioned at the time.
Whether an Eagle kit could be converted to any of the other ships in the class would depend on how picky the modeler was. All five of them differed significantly in length. I don't have all the dimensions in front of me, but if I remember right the Horst Wessel (later Eagle) was about twenty feet longer than the Gorch Fock (later Tovarisch).
One source of confusion about all this has always been the set of plans drawn by the late, great Harold Underhill. He made those drawings in conjunction with his book, Sail Training and Cadet Ships. He was working from the original plans of the Gorch Fock. In the text of the book, Underhill gives the lengths of all the ships in the class, and is completely up front about the fact that the plans only represent one of the ships. Unfortunately the plans have been sold by several vendors over the years as representing the Eagle. It's my understanding that, with the notable exception of the Imai 1/200-scale kit, every commercial Eagle kit ever produced (including the old Revell one) has been based on the Underhill plans. (I don't know about the Mantua one - but frankly I have yet to see a Mantua kit that merited the label "scale model.")
Another problem is that the Eagle has undergone many modifications in the course of her career - modifications ranging from armament (she carried a few anti-aircraft guns in her German years) to the change of name on her wheelbox to the construction of a deckhouse at the break of the quarterdeck to the painting of the "Coast Guard Slash" on her bow to the addition of a mass of antennas on her mizzenmast - and big electric floodlights at the top of each mast, to illuminate the deck during on-board parties and ceremonies. I haven't seen her closeup since I made that drawing in 1994, but I'm quite sure she's changed in some noticeable way since then. The kit manufacturer would have to be careful, and determine just what configuration the kit was to represent.
I agree completely that the Eagle would make a beautiful subject for a 1/96-scale plastic kit. (Believe, me, though: plenty of traditionalist ship modelers do think wood is the only "legitimate" material for a ship model - regardless of what material the real ship was made of.) Maybe one of the big manufacturers will read this thread and spring into action. And if anybody thinks that's actually going to happen - well, I can also get you a good price on a bridge in Brooklyn.
Youth, talent, hard work, and enthusiasm are no match for old age and treachery.