The building of full-size ship replicas is a complicated subject - and among professional historians and preservationists it's an extremely controversial one.
People who haven't tried it almost invariably underestimate the difficulties of such a project - starting with the cost. As an example, a group of enthusiasts near my home decided they wanted to build a full-size replica of the gunboat C.S.S. Neuse. (The remains of the original hull have survived, but they're in terrible condition; the idea was that the replica would show the public more effectively what the real ship looked like.) Their first call was to a lumber dealer, whom they asked how much it would cost to buy the necessary amount of oak, juniper, and other types of wood necessary to reproduce the frames and other structural members of the ship. The bid was something over $1,000,000. So they started looking for ways to compromise - changing the frame spacing, making the structural members lighter, etc. They've now just about finished the hull. It doesn't look bad from the outside, but the interior bears only a vague resemblance to the actual ship.
Then came the question of the iron plating. They gave up on that completely; the casemate on their replica is going to be "plated" with painted plywood. Then come the questions of the guns, the engines, etc. The finished replica will look something like the real Neuse from a distance - and may indeed be a valuable teaching aid. But it won't satisfy any reasonable definition of historical accuracy.
If the replica is to operate, it's going to collide with modern safety standards - for good reason. The tragic case of the first Pride of Baltimore comes to mind. Watertight bulkheads, life preservers, and communications gear are necessities for modern operating vessels, but they play havoc with historical accuracy.
A replica of the Hartford would create even bigger problems. The wood for her hull would be at least twice as expensive as that bid for the Neuse replica. Reproducing the engine would, to all intents and purposes, be impossible. The rigging would require hundreds - maybe thousands - of cast- and wrought-iron parts which few people nowadays know how to make. And getting somebody to cast a set of Dahlgren guns....Folks, forget it. It's just not going to happen.
Many historians and preservationists turn up their noses at replicas. Such people point out that, especially in these rather trying times for such projects, there's only a certain amount of money available. State historic site budget directors and philantropic people have to decide where that money is going to go. It's often argued that actual, restored ships and maritime museums ought to have first claim on the available funds. I'm aware, for instance, that a group in Philadelphia has been trying for at least twenty years to raise the money for a full-size replica of the frigate United States. I'm sorry, but I'm opposed to that project. Aside from the fact that such a replica would be extremely similar to a certain honest-to-goodness ship currently moored at Boston, the city of Philadelphia already has a maritime museum and several preserved ships (most notably the U.S.S. Olympia) that never have enough funding. If wealthy Philadelphia maritime history enthusiasts are looking for places to put their money, there are more than enough already without creating a new one.
My own personal opinion is that replica ships can in fact be done well, and do have perfectly legitimate functions that can't be performed by anything else. I'm a big fan of the three replica ships at Jamestown, the Elizabeth II, and several others I could name. A reconstruction of the Santa Maria in my home town, Columbus, Ohio, isn't bad; it escaped the Coast Guard's requirements because it's permanently moored to a pier in the mighty Scioto River. And the reconstructed Greek trireme Olympias has been a priceless source of information about how ancient warships worked - or didn't work. In general, though, I'd rather see the money go to the restoration of real ships, and to maritime museums that exhibit real artifacts, than to "replicas" of dubious authenticity that, for entirely real practical reasons, simply cannot adhere to any standards of historical accuracy.