Transporters work by de-assembling something (e.g. you) and re-assembling it somewhere else. What if, when you're dis-assembled, you die, and the re-assembled version of you is essentially a copy? Then every time someone steps onto a transporter, their final thought before death is that they'll end up beamed somewhere else. And the re-assembled version (copy) just thinks that everything went fine and continues on like nothing bad happened.
The original version of me ceases to exist, but for all intents and purposes there has no been no break in existence for [OmegaMouse]. You could say that those are two separate people, but what if the same happens every time we go to sleep, and we’re none the wiser? As long as someone identical comes out on the other end, what difference does it make?
It makes no difference in the sense that a version of you would still exist, but for the version of you that ceases to exist, I’d think it would matter to them. The movie The Prestige from 2006 somewhat illustrates my point on this.