Yes it makes sense. It would motivate them powerfully. But it’s been done too many times, and it’s too easy.
The rule makes you find more interesting ways of motivating them. Are they driven by bruised pride? By romance? By obsession? Anything is more interesting than rehashing the cliché Hollywood loves.
Similarly, don’t make a villain more evil by saying “they’re a dictator and also a kiddie-fiddler orremoved”. That’s just tacking on villainy.
That would be like having a right-wing US President, and saying “oh he’s also aremoved and best friends with a child-trafficker” - lazy, unrealistic writing. Make your villains more nuanced please.

The Culture average skin tone in humanoids is a lot closer to Black than white, but race doesn’t really exist as a culturally meaningful category for them. The only time it comes up is some Azadians making shitty remarks about Gurgeh.
i’ll give you two guesses what the actors in any mainstream adaption would look like.
One of the many reasons nobody with the resources to make a Culture adaptation could ever be trusted to do so