Firstly, the story of diablo 3 would have been the same regardless of whether aidan was related to leoric or not.
Prior to the events in diablo 1, leoric was going mad and killing his own loyal subjects and even killed his queen. Throughout all these his son was away on some business and did not come home to see wtf was going on? did none of leoric's men send a message to aidan telling him what was going on in his own home? what business was aidan on that was so important anyways? his kingdom was at war with westmarch, but the prince goes somewhere else for no reason. Even after both his parents have been killed, Aidan STILL did not go home, it was not until demons started swarming in the cathedral and leoric turned into the skeleton king did Aidan come home. How does this make any sense for him to be Leoric's son???? It only makes sense if the hero was in no way related to Leoric.