Dave,
I don't think that panel is too small for all those wires. I think that they look horrible because visually they just look like a bit of a mess.
A neatly organized, but packed, panel can hold more than an unorganized and less full panel. The same thing applies to junk drawers and computer cabinets. I went looking for examples of origami wiring in computer cabinets, but ever since Microsoft came out with a computer they call "Origami" all the Google links go there.
The basic idea, however, is to run all the wires as parallel as possible, then make right-angle (or sweeping curve, as required) bends. With data cables, we use things that are closer to origami techniques than anything I learned when I was an electronic tech decades ago. The result is that things stay in place and out of the way of everything else, much better. The benefit for computer cases, for anyone who cares, is that airflow through the case is dramatically improved.