>>713282551 (OP)>She had a hard life>She had no agency>She deserves to be happyThat's pretty much it. A lot of people tend to sympathize with those who were forced into terrible situations through no fault of their own. Sakura was a character designed to garner pity. Every single attempt she made to improve her situation or resolve the issue backfired on her spectacularly. She's a hopelessly sad and pitiable character that people want to see saved. She bypasses the basic need for charisma or self-actualization because of this.
Other characters might have their own sad situations, but most of them had more agency than she did. So as miserable as Saber's existence is, the fact that she chose her path by becoming king makes her inherently less pitiable than Sakura. Subsequently, because Saber is a stronger character who chose her fate, it's okay to sacrifice her for the more helpless entity.
Basically, people tend to root for the underdog, and their actual characterization matters less than the amount of suffering they endured, and there is no bigger underdog in Fate than Sakura.