Aye, and it wasn't just in medieval times. A perfect example is how the UK ended up with German-speaking kings. If you think of your "non-family" generals as actually distant cousins instead of non-family, then it actually makes the situation even more historically realistic. Think of adoptions as your faction leader bringing distant relatives, still of royal blood, into the immediate family as wards. Very few direct lines of descent managed to survive in Europe, with the ruling family of Monaco being about the only one.