On the contrary, conquest is the foremost and supreme claim to the throne that superceeds all others. If kings are appointed by God, and rise or fall by his hand then one can only take and hold the throne by the grace of God no?
At least, this is how legitimacy for the throne is or was previously drawn in European states, and remains so in England. It would rather shake things up were it not because like you allude to yourself; Edgar despite William and Harold's claims would be the true successor.
And William/Harold/Harald are not even the earliest example of authority drawn from upsurping a previous royal house.
You can't really claim Catholic sanction to deny it either, since the Papacy recognises this type of authority above bloodlines as well (see the Papal coronation of Napoleon and the wider House of Bonaparte).