Alfred the Great was extremely popular. He established a model of kingship in England that was built upon by his successors, and copied by later conquerors. Alfred established fantastical roots both for his kingship, and for the Anglo-Saxon people, tying them together with Christianity as glue in the Anglo-Saxon Chronicle. He rallied all the petty kings in England under his own West Saxon aegis, and became the first king of the English. He began a campaign of literacy and literary production to bring England back to the glory days of 8th century scholarship, when England led the world in learning. He and his successors adopted Carolingian models both for kingship and for monasticism (i.e. the Benedictine Reform), tying politics and religion together into a theocratic form of rule. He was a genius, and his work was so far reaching that he set a course for what England would be that in some ways even withstood the flood of Norman politics and Anglo-Norman culture that would later come to dominate the island.

People tend to forget that Cnut the Great took the kingship before William the Conqueror. There were two instances of domination by an outside force, not one, and they came in relatively rapid succession. Cnut and William the Conqueror had very different ways of ruling the country though. Cnut modeled himself after the English kings, and prime among them was Alfred. He wrote laws in a form similar to what came before him, and styled himself after English kings in many ways. See Cnut's Letter to the English to see how he reaches out to the English and connects back to Alfred's English lineage by saying that he will uphold the laws of Edgar. Cnut knew that Alfred and his successors were extremely popular, or at least some of them were, like Edgar, who was in many ways carried on Alfred's program of politics and culture better than any other English king, so its no wonder that Cnut singled him out as his model lawgiver.

William handled things quite differently. He dominated the English from afar and sent barons in his stead to rule the country. He built churches in a very different style overall, and changed the laws of the country dramatically. There are poems in the AS Chronicle that complain about his style of domination and note that he changed the landscaped entirely by building new buildings everywhere. This is an instance of one kind popular sentiment finding its way into the history books.

So why then would later kings take up Alfred as a positive figure? In my view, it is because they had no choice and it was advantageous for him. Alfred had long since become a figure in the popular imagination, and tales where told about him. He was a big enough figure that there are four MSS from the 13th century, in early Middle English, that preserve a text called The Proverbs of Alfred. He was such an important figure that he was seen as a font of gnomic proverbs even 250-300 years after his death in England. That's a tide you can't push back, no matter what. So later kings incorporated Alfred into their political and social programs.

Take a look at David Pratt's The Political Thought of King Alfred the Great for details about Alfred's political program, with special attention to the role of learning in his model of kingship. Elaine Treharne's Living Through Conquest: The Politics of Early English looks at the period of the conquests using the status of English to focus her discussion of the history of the period.