the phantom has provided the clue that remained obscure to me all of these years. Whether or not Aragorn carried another weapon or fought more like Jackie Chan, I'll leave for another day. The reason, now obvious, that Aragorn was carrying Narsil was that he and the rest of (what will make up) the council were in an
endgame. Sauron's Ring had reappeared. Either Sauron would be vanquished, or he would overrule all of Middle Earth. Sure, Narsil might increase the number of visitors at Michel Delving, but it might be of better service in the hands of the heir of the Sauron-bane. Why not? Was the idea to see how the Sword would react (and vice versa) to the Ring when the two were proximal? That's an experiment I'd like to see.
And, as stated, who would get the shards if Aragorn died? He would begat no heir unless he destroyed Sauron. Elrond, sooner or later, was leaving Middle Earth, as was giving away those things that were to remain in the east. What a yard sale that would be!
It all makes sense now. And PJ didn't have the better idea...phew!