One of the nice little details in TWOK was when Kirk and Saavik carried on their conversation while disembodied in the transporter beam,
when beaming up from the Genesis Cave. The idea that life continues uninterrupted during transport was of course taken to the next level in TNG: The Realm of Fear
. The transporter not interrupting any biological process at all, including cognition and consciousness, could be one portion of a convincing argument that what comes out at the other end really is the original.
But some level of injury should be expected from transporter use; no mode of transportation in the real world is perfectly
safe, not even walking. One of the nice little details in TMP was the addition of the radiation shield in the transporter room, to protect the operators from repeated exposure to some sort of radiation. Perhaps, if a person were repeatedly beamed enough times, with no breaks in between, eventually they would get sick. Maybe cancer would be a risk from too many beamings too often. While they didn't use Federation transporter technology, the terrorists who transported via dimensional shift in TNG: The High Ground
suffered warped DNA which was cumulative and terminal on repeated use. Then again, as has basically already been pointed out in-thread, no activity in life whatsoever is perfectly free of risk. Because Geordi quantifies [in terms appropriate for TV show dialog] what he means by the level of safety, among my favorite TNG snippets is from The Masterpiece Society
MARTIN: We have no idea how molecular transport will affect her DNA.
LAFORGE: It won't affect her DNA at all. There's been over a century of evidence to prove that.
And, whether I'd do it willingly would depend in part on what sort of argument was being made that the original me would be coming out on the other end. A portion of the risk of use would be the risk that one or more of the scientific theories upon which that argument is based is wrong. Those theories should be very well
tested, so that the probability of any of them being measurably wrong is vanishingly small. Biological processes theoretically continuing uninterrupted throughout beaming could help make a convincing case that the original me would be coming out.
Of course, if the ship were blowing up around me and there were no other chance, I'd probably shout "Energize!", even if I would be the first person to beam.