Your point about training density is well taken and I should have said that in my last post.
Pullups are a unique beast for this example, though, because it would be a rare thing to say the least to see someone perform 100 unbroken dead hang pull ups, meaning training density will almost always come into play for those.
But things like band pull aparts, face pulls, curls, what have you, are all going to be easily accomplished even after you reach maximum training density (100x unbroken). In order to increase performance in that movement, you will need to add volume or loading. There's no other way around it.
And even then, you have to wonder WHY you would be doing such a thing. I look at training as having a goal, rather than being the goal in and of itself. Every movement and training parameter should have a specific relationship with your training goal. If you want to be the unbroken pullup champion, it makes a lot of sense. If you are trying to improve your deadlift it makes less sense. The movements are very different, so you can't train it as a SPP movement. At best, it would be an accessory/assistance. And in that context, It makes little sense to do the movement 100x a day every day and only worry about training density. To me, that sounds like a greater emphasis on GPP and work capacity than on improving SPP or even related musculature.
Now, if you are just doing things to do it - then everything works. So, there can be no failure. Yes, training pullups, regardless of density, every day is "working out" and you will be in "better shape" than you were before. If you are increasing your training density, you will see benefit in hypertrophy, too. In a certain context, everything "works"
But, as Csulli alluded to in his second post, if doing 100s a day is such killer method for everything, why not just do all your compound movements 100x a day, every day?