Daystrom Institute

Doctor McCoy used the transporter very frequently with minimal complaining; the only complaint I can recall is from TMP and followed a horrific and unexpected transporter accident.

As for transporters in Enterprise, two things are especially noteworthy: one, they explicitly refuted the idea that the transporter creates a "some sort of weird copy" of the person or object transported, and two, those human-safe transporters were contemporary with very primitive replicator equivalents called protein resequencers. Clearly transporters aren't building humans atom-by-atom from data alone if they can't figure out how to do more than resequence protein molecules in any other context.

Transporters don't do anything to affect the matter they are transporting unless explicitly intended to: by the 24th century they are programmed to filter out recognizeable pathogens, and can be used to deactivate weapons or occasionally monkey with the genes of a person in mid-transport, but things routinely pass through the transporter without issue which are either totally unknown or explicitly non-replicatable. None of this makes sense if the sequence is scan -> destroy -> rebuild, but makes total sense if the transporter is shifting the transportee into subspace (with some tweaks to allow them to exist there) and then back out of subspace at the destination.

Thomas Riker (and now William Boimler) is the one big exception. Both occured under a very specific and extremely rare weather condition, and the first time this happened the Chief Engineer on the flagship of the Enterprise was shocked that such a thing was even possible. I'm much more inclined to believe that the "transporter duplicates" are actually the result of the phenomenon that duplicated Voyager in Deadlock, not the transporter actually constructing two people from the pattern and matter of only one.