The princess doesn't need to be saved. Or want it.
It turns out that Emperor Evulz was granting Princess Velvet asylum to protect her from her brother, PrinceSatin.
Princess Velvet and Emperor Evulz are in love, but her father the King would not consent to their marriage. The kidnap is an excuse for them to elope.
The princess doesn't need to be saved... at first. But she winds up in serious trouble before long and has to be rescued by the hero after all.
Emperor Evulz is granting Princess Velvet asylum to keep her safe from Prince Satin, but he can't confront Satin directly without risking a huge, bloody war. Albert can and will, and with his help, Princess Velvet can finally return home safely.
Emperor Evulz doesn't even have any plans for Princess Velvet. He just collects princesses as a hobby.
Zig Zagged: Albert hears that Princess Velvet has been kidnapped and comes running to help, only to find that those were merely rumors and she's actually gone undercover and joined La Résistance. But he accidentally lead Evulz' men right to her, and she's captured. Velvet then manages to escape before a rescue attempt can be launched — good thing, too, as Evulz ambushes her would-be saviors and arrests them, forcing her to rush to save them before they can be executed.
Averted: Princess Velvet never needs rescuing.
Enforced: "Okay, he's evil, but that can't be the only reason why our hero wants to stop him! Let's give him a potential Love Interest and have her get kidnapped! Plus, hey — built-in Standard Hero Reward!"
Lampshaded: "Why do the villains always kidnap the princesses? Wouldn't it make more sense to kidnap somebody who is an actual threat to them?"
Emperor Evulz kidnapped Princess Velvet specifically because he knew this would draw heroes out of the woodwork to save her, helping him single out and dispose of troublemakers all the easier.
Or the heroes set up bright lights around the Princess so Dr Evil will come and kidnap her and catch him.
Defied: Emperor Evulz makes a point of killing any princess he gets close enough to.
Discussed: Bob and team are going to the palace and on the way discuss the chances of there being a princess and how they would save her from Dr Evil.
Conversed: Bob and Alice watch a television show with a Save the Princess plot and talk about it.
The princess resigns due to not being able to rule the kingdom well when she's captured most of the time.
Emperor Evulz kidnapping Princess Velvet and upon realizing he has absolutely no use for her and that she's more trouble than she's worth he kills her and has the hero trapped in the castle when he comes to rescue her.
Reconstructed: After Princess Velvet resigns for being repeatedly kidnapped her evil brother Prince Satin takes over and rules. She gets a Mentor and trains over the years. When Prince Satin eventually becomes Emperor Evulz and kidnaps another princess, she goes to rescue her using all of her genre savviness.
Plotted A Good Waste: Princess Velvet turns out to be the mastermind behind it all, deftly maneuvering herself into the perfect position to secretly steal all of Emperor Evulz' power while he was preoccupied fighting off the hapless heroes trying to rescue her.