Pretty sure the studio just didn't know, after all it was revealed to be a boss drop in Vol. 10.
Usually a boss drop is better than a random drop, in a Liz SS she mentioned that Dark Repulsor+39 (which is equivalent to Elucidator+39) can be exchanged with sword+20 from the front lines (currently 70th).
Using that as a measurement, Elucidator would be about as good as his sword+19 (in the anime), but it was also mentioned that Dark Repulsor could be enhanced 50 times, with such a high number being rare among weapons.
Anneal Blade had a limit of 8, my guess is that at the 50th floor swords have a limit of ~20-25? So unless Kirito enhanced it to the limit, he would use Elucidator.
But if he enhanced it to the limit, he must have used his sword for quite a few floors, so it is about time he exchanged it anyway. If he was using a relative new sword for the last few levels, he couldn't have enhanced it as much, so once again it would make sense to use his boss drop.
Another reason why the staff just missed that detail, from the intro at 56th floor to 59th floor, it looks like Kirito was using the same sword (the handle&guard looks exactly the same), so for the last 3 floors he was using&enhancing an old sword when he had a strong&new sword in his inventar? Very unlikely.
Edit: When I look at my post I didn't realise I was writing so much
