I see the point of this type of 'greasing the groove' working out, gets you used to the movement, and it's probably really good for maintaing a fitness level.
But if you want to increase total amount of say, pull-ups, is it better to go to failure 2 or 3 times with a short rest of say 2 mins between sets, then rest a couple of days to let the muscles rebuild stonger, then either go back to 'greasing the grove' till it's been a week and repeat the max reps to failure, or just do another max reps till failure as soon as the soreness has gone?
I have found that if I just knock out a couple of pull-ups here and there through the day I never really get sore the next day and I'm not convinced my strenght is improving unless I'm getting some DOMS to show I've worked hard enought to need to get stronger (rather sore in my abs, pecks and biceps today )
You know all those pictures of Adam and Eve where they have belly button? Think about it..................... take as long as you need........................