Here's the thing: you're destroying yourself and creating a clone.
You can destroy yourself and create two clones. Or three clones. Or seven billion clones.
In this case you're (probably) using the same atoms that you started out with, but in a true teleporter, you're using different atoms (storing them in the buffer for whenever an incoming teleportation arises). Which means the clone is
entirely different.
Of course, matter constantly cycles in and out of the body normally, but that's different. That's an ongoing process. This is a distinct destructive event. There's no getting around it: You are destroying the original and creating a new entity. It may be an entity that thinks it's the old entity, but it's still a different entity.
The other issue is how the device works, and the problem isn't necessarily the information storage/processing. You could be able to deal with that, provided a powerful enough computer.
The problem is the actual dissasembly/assembly mechanism. Star Trek just used a glittery light beam, but a real device will actually have to work in reality. And the problem is, people don't like being cut in half. And that's not so much of a problem for the original subject (you're killing that person anyway), but it will be for the recreated entity- because the half-finished clone would be effectively be cut in half (or cut into several pieces, or lacking most tissue, or whatever), and during an ongoing assembly process would easily die.
And the clone(s) will never be identical to the original. The best you can hope for is "sufficiently similar". There's all sorts of minor amounts of rare metals and little atomic differences and stuff that would probably be a pain to replicate.
Why would you kill the originals? Just upload "blueprints", then assemble them at destination. You can even run simulations of their minds during the journey, so they're "in control" as a regular crew would be, and preserve all the memories of originals and the journey itself.
Maybe because these people actually want to travel to another star instead of sending their clones there?
If you're running simulations of their minds (for whatever silly reason) they wouldn't need to be in control anyway. Interstellar spaceflight would mostly be boring.
Just freeze them, put them in special cradles and hope they can sustain the accelerations. There's no reason for cloning people or killing them or running mind games or such silliness.
