So in one respect it goes beyond being able to keep the Law, it was designed to teach not to save.
Yes, it would quickly become apparent to the average sinner that it was literally impossible to keep the Law, and that there had to be a deeper message; law cannot save. This is expounded well by Samuel, as well as in the Psalms and in various prophets.
Would "understanding" this fact make it more difficult to keep the Law? And did this in turn cause the pious Jew to make it something (their own) which could be kept?