Or HaChaim on Genesis 36:31/אור החיים על בראשית ל״ו:ל״א

1 ואלה המלכים אשר מלכו בארץ אדום, And these are the names of the kings who ruled in the land of Edom, etc,. The Torah enumerated all who intermarried with Edom or supplied kings to Edom to tell us that ultimately they too would be destroyed when Edom would fall. Bereshit Rabbah 83 explains that because Bazrah provided a king for Edom (verse 33), it too would ultimately share the fate of Esau because it had helped Edom to its feet again when it had already been close to annihilation. Isaiah 34,6 refers to that time when G'd is described as killing many in Bazrah, linking it with the slaughter that would take place in Edom. The same applies to the other cities mentioned in our chapter.

2This chapter also alludes to the ultimate redemption of the Jews which will be a long time arriving; this is why G'd listed the number of kings who would rule over Edom who in turn preceded the kings of Israel. The author expresses the hope that just as after the destruction of the Temple we experienced a series of kings who ruled over Edom, this in turn would be followed by a series of kings ruling Israel until such time as the final redemption (6000 years) would materialise (based on the assumption that the period of ימות המשיח is the seventh millenium; compare one view in Sanhedrin 99).