It isn't just the thematic implications (see above link), it's the poor writing.
As I state about the Ring from Lord of the Rings, either the story's problem is a problem or it isn't.
A common problem in a romance is the tension created between the characters' love for each other versus their circumstances--Romeo & Juliet, basically, only the intrusive circumstances are not always warring parents.
Sometimes the intrusive circumstances are different religions. Or different socioeconomic circumstances. Or different goals in life. Or different obligations. An honest writer will honestly present these circumstances. Character A, an actor, can't decide whether to give up his dream of Hollywood to stay in the cozy-hometown of his lover (Character B). The princess (Character A) has no intention of giving up her royal obligations to ride around all day on the moped of her lover (Character B).
|In Roman Holiday, the story is more the journey|
|than the romance.|
The writing problem occurs when the writer realizes, "Oh, I wrote myself into a corner here. I guess at least one or maybe both my characters aren't THAT dedicated to their goals and beliefs. They are willing to give up what they want."
I should clarify that this ending can work--IF the character who gives in/gives up was already heading in that direction in the first place. Dorothy realizes that she truly always loved home. The actor recognizes that he kind of hates Hollywood and would rather do local theater productions. The princess--
That's a harder one.
Dating a prince or princess is a common romance trope, and like the Hollywood trope, it often fails because a prince or princess is not going to abandon national obligations for the sake of a love affair.
Or, rather, the kinds of princes and princesses that we actually respect aren't going to. Edward can swan off to marry Wallis--and everybody heaves a sigh of relief--but Edward doesn't make for good romance fodder, not unless one entirely alters his fundamental personality.
That is, if the prince or princess is going to be the type of person who takes royal duties seriously--which creates the romance tension in the first place--having that prince or princess decide at the end, "Oh, I don't really care THAT much" undermines the entire tale. If it never mattered that much, why was it an issue in the first place?
This is the Grease ending. If all it takes is two people turning themselves into a reflection of the other--well, that was 2 hours that didn't need to happen. Why didn't we just listen to the album and not bother with the plot?
It can be difficult to write oneself out of an impossible set of circumstances. Generally speaking, it might be best to use the "hey, my character was already heading in that direction" solution. So--Danny didn't turn himself into a "letterman" merely to get the girl. He was actually tired of leather and will go on to graduate cum laude from Stanford.
Such a solution wouldn't be too difficult to set-up--just a tweak to the dialog.