I've played both the Imperial side and the Republic side through Taris and the idea of saving Taris seems silly to me.
So, the Imp side wants it fully destroyed to "remind the Republic of it's failure." The Republic politicians want to save Taris, thinking they can reclaim it. What's funny about that is, if you talk to most of the Trooper npcs, they wonder what the point is too.
I personally side with the Imps. The planet just needs to be put out of its misery. When the Republic finishes its studies, they should bail out too. The planet seems so damaged it's beyond repair.
The arguments for
reclaiming Taris are explained when you first arrive on the planet, and now that the Republic actually started with the work they have to see it through. It now must either become a symbol for the Republic or for the Empire. Any consideration if it was worthwhile to sink in billions of credits into the project have been made before the project started and are now largely irrelevant. The only reason the Republic can give up is when they have bigger problems that make losing this propaganda battle against the Empire seem insignificant. At that point it truly has become pointless as the Empire will have effectively won the war already and Taris is just a footnote in the story of that war.
The second, unvoiced but much more pressing, reason to go on with the reclamation is that Taris in its current form is pretty much a zombie factory chock full with an incredibly valuable hoard of metals, precious and regular. Scavengers will
come to the planet and sooner or later they will
bring the plague off world. And if not them then the Empire or another lunatic hell bent on galactic domination will seek to weaponise the rakghouls. With a disaease that virulent and that mutable it will fail as a weapon but it will still cause the death of triillions of people and turn any planet effectively uninhabitable that gets infected.
So the Republic needs to establish a foothold there and study the rakghouls and ways to contain or erradicate them. Before somebody else does the same and dumps a few dozen rakghouls on each of their major planets.