It's been done, though. Even before "Measure of a Man", they use Picard's extant transporter pattern to reincorporate him in "Lonely Among Us".
But the idea there was that he had two parts, which were referred to in the episode as his "physical pattern" and his "energy," with the latter being where his actual consciousness resided. I have my problems with that terminology, but the intention was that it was possible specifically because the aliens' nebula was preserving the important part of Picard and the transporter just held a more limited portion. I like to think that it was his actual transporter pattern, the energy matrix defining the structure of his brain and body, that was preserved in the nebula in the same way it would be preserved in the pattern buffer, although for a longer time, whereas what was stored aboard the
Enterprise was the actual particles that made up his body and the "transporter trace" mentioned in "Unnatural Selection" that gave the transporter a basic template for the reassembly. But those couldn't have been put together into a live Picard until the primary pattern was recovered.
That, or it was just a weak episode before they'd quite figured out the rules and we shouldn't take it too seriously.
And later, in DS9: "Our Man Bashir", they store the entirety of Sisko, Kira, O'Brien, Worf and Jadzia Dax in the station's computer when the transporter fails - albeit with severe consequences for the station's short-term functioning due to a lack of memory for anything else, but that was because it was an unplanned bodge-job. If they planned for it, there's no reason they couldn't have a crapton of RAM standing by to do the storing and churn out as many Tom Rikers, or Datas, as you want.
But of course, if you're the writer (or the audience), that's what you
don't want, because then nobody ever dies again and there's no danger and the very nature of existence is changed unrecognizably and that would make for pretty crappy stories. So while the rules may be occasionally bent to allow such things to happen as freak accidents, it's best to assume that they aren't something that could ever be done on a regular basis, at least not during the era of any
Star Trek series. If an episode like "Our Man Bashir" gives the impression that it's just a matter of having enough memory, then that's a shortcoming of the story and is not something that is desirable to embrace.