I don’t use a liner either, I just use hay to scrub/wipe most days when I am just doing spot cleaning. I have a grubby wash cloth for deeper cleaning too. Basically just layer of Yesterdays news and the layer of hay, which I spot clean every other day unless someones been very busy. He has two boxes, actually 3 as I just got him one for deck, so it gives me more wiggle room, I just toss the soiled hay and litter in a paper shopping bag and when that’s full throw the lot in the compost. Every other week or more often if it seems like it needs it, I toss the whole thing and give it a serious scrub with some mild soap and hot water, and let it air dry in the sun or use an old rag to dry. I did use paper liners in the beginning, but found if anything they made the whole thing messier and harder to clean. Made it smell worse too, but that could have been my experience.
I guess I am still wasting the paper bag in the intermediary step, may think up a less wasteful method, but for a while had an over abundance of grocery bags as stores weren’t letting you bring your own. (The still don’t, but now I have them just stick it back in the basket and then bag it outside).