Sure they could make a a NEW Tuvix, but I suspect they couldn't make the same Tuvix.
Reunification would have been like if parents who lost a kid named Barry, creating a backup replacement and also called HER Barry pretending that there had been no Mulligan.
Tuvix's soul?
Tuvix in Chakotay's animal guide technopot vision quest machine?
Would Tuvix have manifested up for the vision quest or Neelix and Tuvok?
The CLOWN!
That clown was made up of several people and Janeway killed him well.
But are holograms alive?
A thought provoking post! In reference to your last question, "Are holograms alive?" I'd like to add a couple more questions--
Would it be morally acceptable to destroy The Doctor?
Would it be moral to keep him as a slave? If we decide The Doctor is not alive, can it still be immoral to keep him as a slave?
Would Janeway pull the switch on The Doctor if it suited her needs? (After agonizing over it, of course.)
I'll let Rod Serling take us out: A fable? Most assuredly. But who's to say at some distant moment there might not be an assembly line producing a gentle product in the form of a doctor whose stock in trade is humanity? Fable, sure— but who's to say?