I see two major issues with the legacy system:
1) basing a perk system/reward solely on same player alts will to some extent lead to "alt factories" - the galactic version of "the more kids, the more child benefit ye shall receive" if you like.
2) having to figure out believable ways to somehow squeeze completely unrelated alien races and stories into variations of "I am your father". The main reason that line worked as a great story plot reversal in the movies is the fact that it's unlikely on an epic scale (but still genetically possible). Making the astronomically unlikely (and genetically impossible) common place (and even enforced in a way) IMHO is not going to be believable and will likely be a straight jacket on RP.
Players should have the freedom to have different characters on the same server that they don't want to be related in a family sense, but still be able to cooperate or interact as a kind of a small, loose consortium/mini-guild/cell, whatever you want to call it.
Let players who want to set up family trees be able to do that not only with their own, but also with other player's characters. That will be much more social and believable.
Bottom line: a completely separate surname/family tree system and "same player mini-guild" with things like perks, a shared bank slot between alts, etc. would be more social + allow much greater flexibility and enjoyment.