One of the mains reasons could be that there wasn't actually as much uniformity among the English nobility as you'd think. By the time the Normans invaded, the territories in England were actually largely controlled by Earls that were descendants of, or at least loyal to, the Godwineson family. Leofwine Godwineson, Harold's brother, was Earl of Kent, Harold and the Godwinesons had more or less complete control over East Anglia since the 1050s, the Earls of Mercia and Northumbria had been supported by Harold in the ousting of his brother Tostig, and thus were loyal to him although they were themselves descended from Cnut).

In fact, it's probably best to think of the rulership of England from about the 1650s on as pitting Godwinesons against the line of Anglo-Saxon Kings. The Godwineson family having always held positions of great power and authority simply by virtue of having been effective rulers and advisers, and the Anglo-Saxon kings obviously holding power largely because of tradition.

So it wasn't so much that William was ousting a bunch of long-standing nobility, but rather a collection of noblemen that had only in the last decade or so been given their Peerage as Godwin became more influential under the rule of Edward the Confessor. England's Earldoms weren't nearly so stable as your question suggests, and this is in large part because of the struggle for power between Edward and Godwin (and his family). Harold had become King, to be sure, but only just. So don't think of them as Anglo-Saxon nobility so much as brand spankin' new Godwineson nobility. The Godwineson family had a very tentative hold on England when it was invaded. Helped exactly not at all by the fact that his brother Tostig invaded TWICE in the days prior to the Norman invasion, because Tostig is a total dickbag.

Marc Morris has an absolutely delightful new book about the invasion called The Norman Conquest. It's a great read!

Edit: typo.