Hiding was an act of cowardice. Maedhros was many things, but he actively fought against cowardice. After he took his own life knowingly and openly, leaving behind a brother to suffer the Ages to come alone, he was determined to stand in the full light of day even if it hurt. Even if it made everyone hate him (as they should in his opinion).

"One is destroyed. I have not asked Kano what he did with his, but his hands..." he grimaced, paling, "They bear the same marks of rejection. He would not have been able to keep the Silmaril on his person and since he no longer has a home..."

Maglor must have gotten rid of the Silmaril somehow, somewhere. Perhaps in the sea.

"The last one can be seen above us all, worn by Eärendil the Mariner."