Laura C asked a question in the comments about what happens when the heroine is the protagonist and hero rather than operating as a co-protagonists operates as a major secondary. Does he have to have a character arc?
I would argue that if two characters are involved in a life changing romance, both of them had best change. If the hero is acting as a major secondary, he might not have as dramatic curve but he will have a character arc. If he can successfully take part in the final climatic scene at the end of the story as the same person he was at the beginning, you don't have a story. Any time you are involved in an emotional relationship, you are changed in some fashion.
Perfection in a character is boring. Imperfection makes more interesting characters. What is your secondary's flaw? What are his fears? Why can't he be with the heroine at the start? What lesson is he going to learn from her? How are you goign to show that he has learnt the lesson and is worthy of the changed heroine's love?
If you look at Romancing the Stone, Jack does change through out the story. He wants to become a better man. He doesn't steal the map from Joan. He is no longer involved simply for the money. He is not the main POV character but he does change and he does decide to invite Joan onto his yacht or rather to share the adventure of his life. He needs her in his life.
Joan has changed the most but Jack has also changed.
If you look at Casablanca, Rick changes the most but Ilsa also changes. They both in their own ways put Paris from them and then have been able to recapture that.
The amount of change a character has to go through depends on the character. the protagonist of a story should always go through the most change, but if it is a romance which forms the spine of the story, then both characters should change. Or otherwise what is preventing the non changing character from having his or her HEA? The change can be small. It may be that the character learns they need the protagonist in their life to be complete bu they should change.
I hope this makes sense.