William the Conqueror Accepted

How would Anglo-Saxon culture have faired if they accepted William the Conqueror as king instead of electing Harold Godwinson?
 
I'll admit it isn't very likely, but maybe they believed that Edward the Confessor picked him (yes I know that the moot has the final word and not the previous king), caving to William's papal support, fear of the inevitable invasion, there are probably others.
 
Why would they vote for him?

Find a way of making Harold really unpopular somehow? Maybe he falls off his horse, bumps his head, and becomes really erratic and violent as a result. Then a significant portion of lords decide that any king would be better than the one they're saddled with but don't feel sure of victory on their own, so they send a message to William offering him the crown if he'll come and help them.
 
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