To the extent he is an historical figure, it wasn’t even David who killed him, as I understand it. Rather it was an appropriation of a the valor of one of David’s own soldiers by David’s biographer/Propagandist/Deuteronomist since seemingly their own sources say that Elhanan killed him:

IN ANOTHER BATTLE WITH THE PHILISTINES AT GOB, ELHANAN SON OF JAIR THE BETHLEHEMITE KILLED GOLIATH THE GITTITE, WHO HAD A SPEAR WITH A SHAFT LIKE A WEAVER’S ROD

2 Samuel 21:19

It seems unlikely that any scribe in a Davidic regime would get away with the reverse; attributing one of King David’s most heralded victories to a lowly son of Jair.