Source for some episode where they talk about how they die each time they use a transporter? Other than McCoy or Barclay being scaredy-cats.
http://memory-alpha.wikia.com/wiki/Replicator
A replicator was a device that used transporter technology to dematerialize quantities of matter and then rematerialize that matter in another form.
There's tons and tons of dialogue on how replicators are just transporters set in duplicate mode.
Actually, no. Nothing is destroyed in-so-far as the atoms being dissipated. Star Trek transporters disassemble your original matter and then beams it (move the original) to the new location using pattern buffers and an "angular confinement beam." Then it remotely reassembles your matter stream into its original configuration. It does this at a quantum level, thus preserving consciousness.
How can you say "consciousness is preserved" when we have a clear cut example of two discrete streams of consciousness being produced:

Whose consciousness was preserved there? Why would you expect consciousness to be preserved when it's computer information being transmitted as a digital signal?