I mean, the Balrog was falling into the canyon, so there wasn't the need to fall down and continue fighting him.The Balrog wasn't able to fly, his wings looks almost destroyed, ruined, and this wouldn't grant him the chance to fly back on the bridge and kill the Fellowship.
Anyway i appreciate what happens, cause the fight during their fall into the cave under Moria was outstanding
The Lord of the Rings: The Fellowship of the Ring (2001)
Why did Gandalf let himself fall down after Balrog scene?
2
I think gandalf fell, not because he wanted to, but because the Barloq had to be destroyed. It was the creature that pretty much divided the Eastern and southern halves of Middle Earth. I think Gandalf felt that if the Barloq went on "living" then the "evil" in middle earth would never have been gotten rid of. He was pretty much the only guy that could kill it and he did what he had to.