And that’s where the mistake lies in my opinion. The protagonist of the Saga is NOT the Skywalker family as a whole, the protagonist of the Saga is Anakin. George himself said it several times. Anakin is the protagonist of the entire Saga. The moment Anakin dies then the main film Saga ends, because its protagonist is dead and therefore there’s nothing more to tell.

George can say whatever he wants, but the fact of the matter is that defining Darth Vader in the OT as a protagonist is just flat-out wrong. Looking at it in vacuum, the films’ protagonists are as follows:

TPM: Qui-Gon
AotC: Obi-Wan, Anakin, Padme
RotS, Obi-Wan, Anakin
ANH: Luke, Han
TESB: Luke, Han, Leia
RotJ: Luke
TFA: Rey, Finn
TLJ: Rey, Finn, Poe
TRoS: “REY!!!”

You can debate some of the specifics here like counting Leia in ANH or Padme in TPM, but the gist is that. Personally, I’d consider Palpatine the overarching throughline, but that’s just me.

I don’t like the name Skywalker Saga because it puts a disproportionate emphasis on Anakin, Luke, and debatably Rey while undercutting the contributions of others like Han and Obi-Wan.