The jury is still very much out on what transporters actually do. But apparently, there's this process of "phasing" involved, in which your matter assumes a new form that happens to be invisible and capable of being shot through walls and space into a distant destination where it will "de-phase" back to yourself. It doesn't really sound as if your every constituent particle actually gets identified or converted into abstract data - which is fine because
a) there'd be an awful lot of abstract data to handle
b) if you could handle that much abstract data, you could also manipulate it for eternal youth or the like, or create copies, or store it for immortality
c) turning matter into data and back supposedly would involve Einsteinian energies, yet transporters sometimes operate with very little power (we've seen a hand phaser battery fire up one)
d) and yes, there's that Heisenberg principle to consider...
If you just move the same old matter from A to B albeit in a somewhat exotic form, then all this copying business becomes so much more complicated that it probably isn't worth the bother, explaining why we don't see clone armies or infinite numbers of starships.
Interestingly, this "phasing" business is present on several other Treknologies, too. In episodes like "The Next Phase", "The Pegasus
" or "Time's Arrow", tweaking with the phase of things indeed turns them invisible and capable of going through walls. In episodes such as "Macrocosm", we learn that phaser (!) beams can transport objects or substances to the target. Perhaps it's a case of the same fictional physics being used for three distinct but closely related purposes?