I will not speak to the matter of whether or not your routine will increase back developement. However, it is not the best way to increase your rep count in Pull-Ups!
Why would you think that doing barbell rows is better than Pull-Ups for increasing Pull-Ups? Their not!
Also, I would never do wide grip Pull-Ups as they increase the strain on your shoulder joints. They do not help Lat developement if that is what you are thinking. The traditional thinking is that a wider grip means wider lats. In fact, a narrow grip means wider lats as you go down lower! If you really want to increase the size of your lats do some static holds on the bar while flexing your lats!
If you want to increase your rep count in Pulls/Chins, there are many ways to do it. One way that works well for me is to do three sets of 75% to 80% of your max resting 3:00 in between each set. At the end of the third set I do one set of negatives and one set of half reps (top half) with a weight belt.
My workout looks like this: 25-25-25. Then 10 half reps with a 20lb wt. belt, 3:00 rest then 10 slow negatives. I did this workout three times per week for four weeks prior to a chin up contest I was in. It worked well.
There are other ways to train to get max reps in chins. However, that one is my favorite. I always recommend training three times per week for four weeks taking off two days prior to the Pull/Chin contest. Do not try to train like this year round!
If you are after more reps in any sort of Chin/Pull-Up count you have to train them often. It’s all about hitting the groove and getting comfortable with the pain!
Best Of Luck,