Besides making me not have to watch Luke try to get with his sister I think it would improve Luke’s character a little bit in ANH because he wouldn’t try to rescue Leia because he likes her, which is what Han does, but because it’s the right thing to do.
I agree, although I would probably leave in the “Princess and a guy like me?” “No.” exchange, because it could also be interpreted as Luke being protective of her given Han’s creepy vibes.