The problem exists but can't be solved. There is an enormous amount of mathematics which is undeniably important, and which is inaccessible to me, because it would take a thousand years to read it. But this is an ineluctable fact. It's not a problem that could be solved. QED could not possibly change the situation.
Nothing can change it.
One man can't absorb all the mathematics produced by hundreds. If you take the collected works of Abel, Riemann, Poincare, Goedel, Thom, and two or three hundred other mathematicians whose work is at least sometimes on more or less the same level, and enter all that mathematics into a proof checker, it would still take many lifetimes to read it all. In fact it would take longer to read mathematics through a QED terminal than it would take to read it in printed form. One of the advantage a teacher has over a book is that you can ask questions that either aren't answered explicitly in the book or you can't find it in the book easily. There really is no limit to how much we could want from such a knowledge representation system.