I am somewhat of a proponent of high prominence peaks myself, as a way to single out potentially impressive peaks. As a general rule, the idea seems to work quite well but I too know of numerous examples where that is not always the case.
Where I live, in Virginia, it generally works quite well in the Blue Ridge Mountains to the east of me. The nature of that range is to have lots of up and downs on the ridgelines and a peak with 1,000' of prominence is likely to appear quite dominant in its region, even if there are more P1Ks within two or three miles. The area around the Peaks of Otter is a good example. Sharp Top is one of the most visually striking peaks in the state and is a P1K. Only two miles away, the next peak north is Flat Top, with even more prominence but slightly less dramatic in appearance. Three more peaks with 400-600' prominence bridge the gap between it and the state prominence peak of Apple Orchard Mountain which has a bit over 2,800' of prominence. From a distance, even a long distance, all these peaks look quite impressive by Virginia standards and definitely support the idea of using prominence to single out peaks. But also, even though Sharp Top is easily the steepest and most impressive looking, from the right angles it is clear that Apple Orchard is the highest and most prominent. And, in fact, nearly every P1K in the Blue Ridge is impressive.
Conversely, to the west of me rise the Valley and Ridge province of the Alleghenies. These are a series of many miles long parallel ridges separated by equally long valleys. Not all, but some of these ridges are quite uniform on their crest. The ridge can run on for many miles with only one ranked peak, with the remainder of the ridge being either relatively flat or gradually sloping, to the extent that it is difficult to tell where the highest point even is. Or it can be a continuous roller coaster of ups and downs, none of them ever dropping 300', or even 100'. And every top can be nearly as high as the one true highpoint. Walker Mountain is a good example. The high point is just over 4,000' in elevation, the only spot on this 70 mile long ridge to be so, and it has over 1,300' of prominence. But to look at it from nearly anywhere, the summit is virtually indistinguishable. It may indeed be the most prominent peak on the ridge, but it is far from impressive or striking. Another Allegheny example is Rough Mountain, a 10 mile long ridge with only one ranked peak, which has 1,200' of prominence, located roughly at the mid-point of the crest. However, this ridge is similar to what you describe for Chicoma. While Rough may be the summit and most prominent spot mathematically, visually, the most prominent and striking peak is easily Griffith Knob, a steep, conical peak that forms the south end of the ridge and drops off steeply and abruptly for over 1,000' itself - but only on three sides. It only has 175' of prominence.
This is why I am also a BIG fan of Tim Worth's steepness lists
http://ned-files.com/ which, at least to my way of thinking, rewards a peak for being visually striking. His "Overall Steepest" lists measure the drop of a peak in every direction at distances of 100, 800, and 1,600 meters then averages all the numbers together. Peaks with lots of high ridgelines leading to one slightly higher spot don't tend to fare well with this system, whereas peaks like Flag and Griffith Knob score much higher. Likewise, Sharp Top still scores very high, justifiably so. Walker Mountain does poorly. Prominence still plays a big role, but more things are taken into consideration. It's some fun data to explore.
Of course, a peak certainly doesn't have to be steep to be impressive, and, likewise, some plateaus are quite spectacular in their own right. In short, I guess it's good to have many ways of looking at peaks to decide their worth.
Rick