You get promoted when you superiors feel that you can do more.
Staying in the same job on a starship is like being held back at school.
More so, Kim was doing an Ensigns job. If he wanted to be a lieutenant then he had to be transferred to a new post. It's a waste of resources to put a lieutenant in a post that can be filled in by some kid fresh out of the academy.
I wonder if Chell got promoted when he took over Neelix's kitchen?