Harry Kim never got a promotion for the same reason no one else did.
After the Maquis crew were assigned by the second episode (which ever episode Torres was made chief engineer), they stayed that rank forever.
Tom got promoted, only after he got demoted, so he finished with the same rank he started.
Of course another poster already mentioned this.
I think it is foolish for an actor to want to up their character's rank considering rank had nothing to do with either pay check or the amount of dialogue you got.
Chakotay was the second highest rank, and I think he got as much dialogue as Kim.
Seven Of Nine didn't even have a rank, and she often had the second highest amount of dialogue in that show.