I certainly agree that the Enterprise should have been saved. But it's not surprising that she wasn't.
The Navy itself does not preserve old ships. So far as I know, the only exception is the Constitution, which is still officially in commission. All the other preserved American warships have been saved, and are maintained, by state and/or private organizations. The Navy transfers the ships to those organizations (sometimes with strings attached; there were rumors that, when the Iowa-class battleships went through their most recent recommissionings, the Navy might raid the North Carolina for spare parts). The World War II ships, with few if any exceptions, spent some years (or decades) in service and/or in mothballs after the war, before they were declared surplus and made available to the preservation organizations. (That's why so many of them are now lacking WWII-era equipment, like radar screens and anti-aircraft guns. That sgear got removed and replaced while the ships were still in active service.)
The Enterprise had the rotten luck to become obsolete almost immediately, because her flight deck was too small to operate post-1945 aircraft. So, though there was an effort to have the Navy save her (like it had saved the Constitution), she went to the scrapyard before the movement among state and private groups really got started.
The big problem those groups usually have when they take on such projects is that they have no idea what a staggering financial burden they're taking on. Even if the ship herself is available free of charge, the costs of restoring her and maintaining her are hard for most people to imagine. And those expenses have a way of increasing as the ship gets older. Right now, the North Carolina (which I'm more familiar with than most of the others, because I know some of the good folks who work on board her) is experiencing, among many other problems, significant leakage due to corrosion, which obviously is due to simple old age. (I sympathize completely. I'm ten years younger than she is, and she's in better shape than I am.) Some years ago the staff worked up a long-range plan that involved towing her up to Newport News, putting her in drydock, and patching the hull. It's since become obvious that neither the ship's private support group nor the state of North Carolina will, in the foreseeable future, be able to afford the millions of dollars that would cost. So, as I understand it, the folks in charge of her are now thinking in terms of building a cofferdam around her in her present berth. (That wouldn't cost as many millions. Don't worry - she won't sink; she's been sitting pretty solidly in the Cape Fear River mud for quite a few years.)
Anybody thinking about taking on a ship preservation project needs to consider the fact that, when the ship was in service, hundreds - or thousands - of men were employed full-time maintaining her. To maintain a preserved warship right nowadays requires an annual budget in the millions of dollars.
I frankly am not optimistic that many, if any, more old American warships are going to get preserved. The ones we already have are soaking up all the available resources - and I don't think the people in charge of a single one of them would tell you that her budget is big enough to maintain the ship properly.
One thing to remember in the midst of all this is that the U.S. has done a better job of preserving its historic warships than any other country has. One of the biggest tragedies in the world of preservation, I think, is that not one single British battleship or battlecruiser exists. The biggest surviving Royal Navy warship of World War II is H.M.S. Belfast, a light cruiser.
Our system of warship preservation stinks in many ways, but it's probably better than anybody else's.