It is true that the regional identity of Northumbria had not totally been gone by 1066, as I cite some contemporary testimony in: What were the Danish-controlled areas of England (the "Danelaw") actually called by its inhabitants? As also suggested by OP, however, it is likely that the successive Northern revolts and its suppression around 1070 eradicated the causes of such identity, a few powerful local Earl family like that Morcar, of Bamburgh and Siward-Waltheof, together with less powerful local magnates (thegns).

I'm not so sure about the regional-political identity of Mercia and Wessex (especially the former) in the wake of the Conquest, but I suppose neither of other possible claimants like remaining family of the Aethelings and Godwines, Edgar Aetheling and Harold's younger brother Wulfnoth Godwinsson and Harold's son Wulf did not have a strong local power base (like the local Earl/ thegns in Northembria) in southern England, at least in whole kingdom scale.

The fact that Wulfnoth had been under custody from 1066 to 1087 itself certainly might show the possible danger of the power of his claim to the throne, but he had already been locked away before the Battle of Hastings, and this situation also roughly apply to Wulf.

The cluster of the estates of the Godwins mainly seemed to located in south-western England like Devonshire, based on Domesday Book and contemporary text like Anglo-Saxon Chronicle, but William also attacked Widowed Gytha, mother of Harold, at Exeter in 1068, probably to deprive her husband (Godwine)'s estate. The Godwins was certainly one of the most rich landowners in pre-1066 England, but neither did they enjoy the undisputable claim of former petty kingdoms.

Added References:

• Barlow, Frank. The Godwins. Hawlow: Pearson Longman, 2002.
• Rollason, David. Northumbria, 500–1100: Creation and Destruction of a Kingdom. Cambridge: Cambridge UP, 2005.

(Edited): fixes the broken link (Really thank /u/Tango-range for making a notice).