Architectural detail: Linen closet organizer

I follow Martha Stewart's instructions for folding towels: lengthwise tri-fold, then in thirds.  But I noticed this can make a crease across the towel, which is on display when it's hanging on the towel bar. 

While considering this (rather trivial) problem, I dreamt up a contraption that would allow me to store towels hanging, eliminating the offending crease. 

[Drawn with Paper*]

I'm not going to build this or anything; it's just an idea.  But if I were to implement it, this is what my dream linen closet would look like:

* I'm pleased with the drawings created in Paper (almost everything looks cute), but my penmanship could use some work.