I wouldn't like the look of a used cloth hanging on a caddy and I don't see what that's better than a banana tree, or leaving it next to the sink or hanging it on a hook.
You need smaller cloths. That is the solution here as you clearly will only be happy if your cloth in on a bar on a caddy.
Like most people are saying, I use a cloth, put it next to the sink or straight in the washing machine. I've never had a caddy and I never will.