Is it important for the plot that Leia is Luke's sister?

Question

As everybody knows, Luke and Leia are Anakin Skywalker/Darth Vader's children. The fact that Luke is his son is important plotwise:

1. Being Anakin's son, the Force is strong in Luke, making him a credible opponent.
2. Darth Vader learns that Luke is his son between Episode IV and V, which explains why he focuses his efforts on his search and his conversion to the Dark Side in Episode V and VI.
3. The fact that the Emperor hides the existence of Luke triggered the decision of Vader to kill him.
4. Ultimately, it plays an important role in Vader's redemption and the end of the Emperor.

In Leia's case, I cannot remember any plot point where the fact that she is Vader's daughter matters. It seems to me that everything could have happened with no change with Leia just being the strong Rebellion leader. Actually, she "became" Luke's sister only during the production of Episode V.

I am looking only for answers about the original trilogy (Episodes IV to VI). The fact that Leia makes (The Force Awakens spoilers)

Kylo Ren the grandson of Darth Vader in Episode VII

is irrelevant for the question.

Answer 1

The reason Luke and Leia's siblinghood was important to the plot was because A New Hope set Luke, Leia, and Han up as a Love Triangle. This caused Luke and Han to be rivals for Leia's affection.

One can imagine the awkwardness of having one's budding Jedi hero be a spurned lover who also must face the humiliation of being saved by the "other man".

Having Luke and Leia be siblings elegantly resolved this Love Triangle such that Luke and Han can become fast friends, Han and Leia can hook up, and Leia and Luke can continue to show affection for each other.

Answer 2

The first thing that comes to mind as to why this was important was the end of ROTJ.

VADER
You cannot hide forever, Luke.

LUKE
I will not fight you.

VADER
Give yourself to the dark side. It is the only way you can save your 
friends. Yes, your
thoughts betray you. Your feelings for them are strong. Especially 
for...

Vader stops and senses something. Luke shuts his eyes tightly, in 
anguish.

VADER
Sister! So...you have a twin sister. Your feelings have now betrayed 
her, too. Obi-Wan
was wise to hide her from me. Now his failure is complete. If you will 
not turn to the dark
side, then perhaps she will.

LUKE
Never-r-r!

Luke ignites his lightsaber and screams in anger, rushing at hisfather 
with a frenzy we have not seen before. Sparks fly as Luke and Vader 
fight in the cramped area. Luke's hatred forces Vader to retreat out of 
the low area and across a bridge overlooking a vast elevator shaft. 
Each stroke of Luke's sword drives his father further toward defeat.

The Dark Lord is knocked to his knees, and as he raises his sword to 
block another onslaught, Luke slashes Vader's right hand off at the 
wrist, causing metal and electronic parts to fly from the mechanical 
stump. Vader's sword clatters uselessly away, over the
edge of the platform and into the bottomless shaft below. Luke moves 
over Vader and holds the blade of his sword to the Dark Lord's throat. 
The Emperor watches with uncontrollable, pleased agitation.

It might be minor, but Vader used that information to prompt Luke into action finally.

Also, If you believe what Lucas says is true about having the entire plot mostly done even when the original 3 started, then Leia having the force was essential for the plots of stories 7-9.

Answer 3

If Luke and Leia were not siblings, then the entire plot would begin to unravel.

It was only dumb luck that Han Solo came along for the ride in the first place. He was simply a mercenary when he met with Luke and Obi-Wan for the first time. All he genuinely cared about was getting enough money to pay off Jabba the Hutt because there was a bounty on his head.

The only reason why the Han character was introduced in the first place, was to transport Luke and Obi-Wan to Alderaan. In theory, he would have been paid for his services and continued on his way. In fact, Alderaan had already been destroyed by the Death Star. This is when the plots of Luke and Han (and Obi-Wan, Leia, Chewbacca, R2-D2, and C-3PO) became entangled.

Without Han's help, then it would be unlikely that Luke and Obi-Wan would be able to rescue Leia alone. She was essentially the glue that bonded all of the characters together. If it wasn't for her being abducted (and sending R2-D2 and C-3PO for help to Obi-Wan), then none of these characters would have met.

Lets look back to the first scene when Leia recorded a message for Obi-Wan. She knew where he was, but didn't have any clue about the existence of Luke. The mission of C-3PO and R2-D2 was to find Obi-Wan, not Luke. It was only dumb luck, or perhaps The Force that brought them together. If the droids found Obi-Wan first, then it would be awkward for Obi-Wan to recruit Luke. Luke was only really compelled to leave in the first place because his family was slaughtered, and he had nothing left to stay there for. If the droids never made it to Uncle Owen and Aunt Beru's farm, then they would have been unharmed.

After the Leia was rescued, by Han and Luke, then a love triangle was formed. The only way to civilly resolve the issue was to make Luke be a sibling to Leia. This easily and definitively resolved the love triangle. If Leia did not have a love interest in Han, then there would be little need to keep his character going after the first film.

What kept Han Solo going through the whole trilogy was the mutual love interest between him and Leia. This connection eventually led to him joining and aiding the rebellion. Without his help, then the mission to destroy the first Death Star would have failed. Luke would have died, and the rebellion would have been ended.

Answer 4

I'm sure it was important to Han Solo. Though the Han & Leia as a couple isn't of huge importance until TFA, it was at least a bit of a big deal even in the original trilogy, and that might not have occurred if Luke and Leia had not discovered that they were siblings...