They more or less do that at the end of Lonely Among Us.
That one is actually among the consistent cases. The dialogue emphasizes that Picard beamed out "energy only", which in terms of later technobabble would mean that his body was still (mostly) left doing figure-eights inside the "pattern buffer" in the form of a "phased matter stream". The trick was in separating Picard's "soul" from that stream (which Picard apparently managed because he had the knowledge of the alien who possessed him, although perhaps UFP science already knew how this could be done, too), and later reintegrating it with the bulk of the phased matter in the buffer (for which Picard probably got some help from the aliens). We have seen bits and pieces of people being taken out of the general phased matter stream, or added - say, parasites or diseases may be removed, or the charge in one's sidearm, or the actual discharge of that sidearm. Separating the "soul" bit is in no way inconsistent with all that. And indeed we see a sort of a repeat performance in DS9 "Our Man Bashir".
"Unnatural Selection" also features mere tinkering with existing matter, with the help of some stored information (in hair follicles rather than computer memory this time), although it handles the actual process rather clumsily. Such episodes merely tell us that the transporter is a powerful tool for future surgeons, rather than a xeroxing machine.
It's "The Enemy Within" and "Second Chances", with their creation of two individuals in place of one, that pose a real problem. Where did the matter come from? Well, <technobabble> is a sufficient answer - but it means that a repeat performance would allow xeroxing. Sure, both episodes have this <technobabble> involve an extremely rare phenomenon that Federation science would probably be at loss to reproduce artificially, or even re-utilize at the original, natural source. But the incidents should at least inspire Federation science to solve the related problems, eventually.
Then again, we already have replicators which are perfectly capable of creating living tissue (say, in TNG "Ethics" or VOY "Emanations"). The only reason people don't use those to Frankenstein a complete living body into existence seems to be that there's no real motivation for that. Oh, no doubt some mad scientist in some isolated lab will
try, and for all we know the experiment has already been made by the time of TNG and has been a splendid success. But it's a clumsy way to give birth to people, and probably just isn't worth the hassle.
Clones seem to be generally frowned upon in the 24th century Federation - or at least humans hate them with passion. But that's clones that usurp lives from living people. A clone that competes with Will Riker for existence is an abomination, as in "Up the Long Ladder" or "Second Chances". But a clone that continues the life of Will Riker where the previous incarnation left it, such as in this putative kill-and-copy version of the transporter, need not be objectionable at all.