Some people with a background in statistics wonder why the coefficients of determination are averaged to give each variable its ranking. Sometimes they suggest techniques such as PCA or related techniques such as ANOVA.
Some sort of ANOVA, with a "value" weight assigned to each input variable, would be ideal here, but such weightings would have to be quite subjective anyway and are probably best estimated by the meta statistics of the statistics gathering process itself, which has to do with how concerned people are with various measures.
The selection of demographic variables here is not at random -- they are contributed to this site by the users of the site. There are, therefore, more demographic variables for those "important" dimensions of society as seen by users of the correlator.
Therefore, some principle components are more important than others. For instance, it may be that an optimal coordinate system for these data would include all incarceration rate statistics in the same principle component. It may even be that the eigenvalue is relatively small for that principle component. Without some weighting of the a priori importance of the principle component the ANOVA algorithm would wash out incarceration's a priori importance vs principle components containing "random" variables (that's a pun for statistics nerds) such as median age, Norwegian Americans as a percent of whites, etc.
Another principle component that has "too many correlations", and which would tend to involve only one or two principle components is percapita populations at each of many, income groups.
Again, if we're really concerned about something we tend to scrutinize it more and have more measurements of its various manifestations. That's why averaging the coefficients of determination as a measure of "influence" (as approximately defined as that word is here) works in the measurement of dominant United States influences.