I have almost always seen toilet paper rolls presented on a telescoping plastic piece when available for use. A few times I have seen them presented on a much simpler solution: a simple rod with an upward curve on one end to keep it from falling off. Typically this is presented as a "rustic"-looking design choice, but it actually seems preferable in every way to the telescoping plastic piece:
Why is the telescoping plastic piece ever preferred?
The plastic (or metal) telescoping device allows insertion into a closed space. The ultimate result is both more aesthetically pleasing and "out of the way" if the insertion is inset into the wall, as it often is.
Toilet roll holders that extend out or otherwise are attached and outwards from a wall tend to have the hook and flap system you're talking about, because functionality has been determined to trump aesthetics and space concerns.