I, too, find it difficult to play through a piece, even one at my level, without mistakes after only a week or two or three of practising.
Back when I had proper lessons, as a child and teenager, I remember we didn't practice many pieces to perfection. We only did that with pieces that were chosen for some recital, or - of course - competitions. The latter could take the better part of a year to practice to perfection, or close to it. The rest was practised to a reasonable smoothness, then we went on to the next piece to learn.
While no one explained to us, back then, the background reasons for things that we were told to do, I have thought about this or that since, especially recently, when I started playing again.
In this case, I believe it takes a lot more than a week or two of patient and *slow* practising to commit certain movements of the fingers and their combinations to muscle-memory. And it is, so I came to believe, only when a whole piece is committed to muscle-memory on a purely mechanical basis, when the music can really soar, when you don't have to *think* about which finger goes where, and exactly how. Especially dangerous, I find, is the time when that process is almost done. You go into some kind of trance, into a kind of flow, listen and watch something within you playing, and then something wakes you up in mid-piece. Then, if you are not quite perfect in that piece yet, you stumble. Like the sleepwalker on the roof ...
But the point here is, perhaps, that by practising many pieces from the collection in proper succession, even if you don't practice every single piece to perfection, you will practice certain bits and pieces, typical problems, to perfection and muscle memory, in many different contexts. I find, after I have been showing my wife and my mother the ropes a bit, with the help of the D01 book, it works, especially because the pieces are chosen by Jean-Francois in a way, that one builds on the particular problems of the one before. And later, sometimes a later piece comes back to an earlier problem, in a new context, with deepens muscle-memory and understanding both. I don't think I have seen a better thought out "school" for guitar before, unassuming as it seems at first glance.
I believe, that there are some pieces worth practising to perfection, and those are the ones that touch you personally a lot. Make your heart sing, etc.
Many of the rest might well be stepping stones - not more, not less.
So, I personally would not worry too much about absolute perfection in many of those pieces, as long as the particular problems are dealt with, and that's what I recommend to my wife and my mother. It seems to work out ok, so far.
Differing opinions are welcome, of course. I always like to learn, too.