Swords in The Hobbit

In the book, they did.

Chapter 4, Over Hill and Under Hill, page 64:

Suddenly a sword flashed in its own light.

(Gandalf wielding Glamdring the Foe-Hammer/Biter)

page 65:

He took out his sword again, and again it flashed in the dark by
itself. It burned with a rage that made it gleam if goblins were
about; now it was bright as blue flame for delight in the killing of
the great lord of the cave.

Why they don't in the movie, is never said. I can think of no in-universe answer.