The whole point is that the signals can't all flow left to right in any reasonably nontrivial design, because the latter will almost always have feedback, and at its fundamental level that is how static memory works.
Even if you draw both gates facing the same way, there is feedback and you still need to follow the signals the other way; but instead of simply turning one the gate in the direction its output is actually going, and showing that structure more clearly, you introduce the extra ugliness and confusion of crossing signals.
Sorry I may have spoken inaccurately. Wires can carry signals right-to-left (as you mentioned - this is necessary in any circuit containing feedback) but the _symbols_ should be drawn left-to-right in a digital logic schematic.
Certainly there are different fields that follow different rules, for example in schematic representation of feedback systems the feedback blocks are often drawn right-to-left. They get away with it because their schematics are generally much simpler--usually a dozen or so blocks, compared to hundreds or thousands in a nontrivial digital circuit schematic.
Also - I am not sure I understand your comment about 'extra ugliness and confusion of crossing signals'. Flipping the inverter backwards does nothing to remove the signal cross, it just moves the cross outside of the region you showed. Note how one of the inputs to your flipflop is now on the right hand side--in most cases the crossing will reappear when you connect the rest of your circuit.
Even if you draw both gates facing the same way, there is feedback and you still need to follow the signals the other way; but instead of simply turning one the gate in the direction its output is actually going, and showing that structure more clearly, you introduce the extra ugliness and confusion of crossing signals.