One thing I've noticed in the past with bodyweight exercises is that my performance improves if I have a break of, say, 4 days as compared to 2 days. I've noticed this with dips and, when I first started training, pushups. Doing them every second day my progress was steady, but when I waited an extra couple of days I could often do several more reps than the previous session.
However for the purpose I mentioned in the OP, I'm not overly concerned about PBs, just muscular back development.....if doing pullups every day would accelerate this I'd be keen to do it.