I'm not the most tech savvy person out there but I'm smart enough to understand that Star Trek transporter technology, as explained, is flawed. Like you said, the end result would be a "copy", not the original person. This would actually mean that you'd be dying every time you were transported somewhere. You wouldn't be reassembled on the other end but rather a different person would be. You would be dead.
And like you said there are others issues such as how matter is reassembled at the destination point. Where do those "ingredients" necessary for comprising a human body come from? Out of thin air? That's not possible. The original matter would literally have to be moved thru the "beam" and then reassembled on the other end, which is sort of how it's done thru a stargate I assume. I do think there's a difference between transporter technology verses stargate technology in the way that matter is transported and reassembled. I'm sure someone will correct me if I'm wrong and to be honest I'd welcome a better explanation of the two forms of travel.
They've talked about the stargates disassembling you at the molecular level and sending that matter to be reassembled on the other side over a matter stream.
If memory serves and my understanding of wormholes is correct, a wormhole merges two distant points in space by folding space. It's not a tunnel per se so there would be no need for taking you apart and sending you through over a stream. A wormhole requires a singularity to merge the two points while exotic matter, which repels gravity, pushes the space within open so matter can pass through from one side to the other without being crushed into the singularity.
If we could actually see a wormhole, it would be like looking through an open door and you'd literally step through to the other side, wherever it may be, as if you were walking into another room. You could reach through with your arm and interact with whatever/whomever is on the other side like reaching through a window. That poop-fest of a show called Flash Gordon on Syfylys used something like that to move between Earth and Mongo. It's not as exciting as the swish/wheeze/splash effect of SG's wormhole so it doesn't make for great TV.
Hyperspace theory suggests a 5th dimension. When you are in hyperspace, you occupy all points in space at once. There's no long flight time in hyperspace travel like we see in sci-fi.
For wormholes to work, I would think the two are related. A singularity with sufficient gravity and mass rips a hole through to hyperspace at two distant points, thus creating a wormhole. That's why I believe instantaneous transport over significant distances will, ultimately, be an inter-dimensional related solution.