I’m on the side of it’s probably not really necessary. I have a dirt floor. If you have a wooden floor, that’s a different situation, you need to do something. But for the sides, a barn Dad built over 60 years ago and never painted is still in good shape. The parts touching the ground were treated but not the sides and framing. The wood has weathered but since it is out of the damp and is well ventilated it has lasted quite well. It was built out of oak that he cut from his woodland and had sawn into boards. So that’s another factor, what is the inside of the coop made from. If it’s wood I don’t see a big problem, if it’s metal that will rust, yep you should paint.
I did paint the outside for appearances, but as far as inside no. Why? Partly it would be a waste of time and money. The chickens don’t care and I don’t either. That coop will outlast me, painted inside or not. I like it not-bright. I won’t say I like it dark, but I want more of a softer light inside. I make a lot of changes down there. I add and take out things as circumstances require. Why complicate a project down there, turning a minor adjustment into one that has to take into account the paint fumes and chicken’s respiratory systems. If you want it painted really pretty don’t you need to touch up paint if you mess it up by making modifications?
Mainly, I just don’t see a benefit to painting the inside. But if you are a person that likes to keep it spic and span clean inside, painting is probably a good thing.