Indeed, you folks deserve citations for my contention that the gravity of final runnings is most important.
I start with DeClerck's A Textbook of Brewing, where in the first few paragraphs of Chapter 13 - Filtration of Wort and Spargement of Spent Grain, he presents data and text showing that "last runnings contain abnormal amounts of undesirable matter". The data in the associated table for that passage shows that Ash and Silica increase by 100 to 300 percent. DeClerck goes on to cite Reichhardt who states that final runnings have higher tannin (polyphenol) content. Unfortunately, that Reichhardt reference is not identified in the 1957 version of the textbook, so I couldn't review that Reichhardt reference myself. I'll take the word of a brewing giant (DeClerck), that final runnings also have higher tannin content.
I follow up with information presented in Malting and Brewing Science by Briggs, Hough, Stevens, and Young. Subchapter 9.8 on Polyphenols states that the quantities of polyphenols extracted, increase as wort pH and temperature increase. It goes on to state that the polyphenol proportion increases in the last runnings, to the detriment of the flavor and stability of the beer. The subchapter also distinguishes between 'oxidized' and 'oxidizable' polyphenols and the fact that oxidizable polyphenols can pass into the beer and become tannins and produce haze.
In subchapter 9.18 of Malting and Brewing Science, Sparging is discussed. The effects of increased pH and temperature are correlated to conditions that extract more polyphenols and silicates from grain. But they note that the wort pH rises 0.2 to 0.7 units during sparging in their trials. What I feel is the most important information in this subchapter, is the chart in Fig 9.15 that shows the pH, ash, and silica content of the runoff rise as the sparge continues. An important distinction is that we know that proper pretreatment of sparging water gives us a liquor that doesn't produce a rise in wort pH. I have repeatedly found that even when acidified sparging water is used at temperatures of less than 170F, extending the sparging and driving the runoff gravity below 4 Brix does result in tannin and silicate in the resulting beers. So, I find that it is final gravity of the runnings has the greatest effect on tannin and silica extraction.