He could have been exactly the same repressed and lovable character without details like regularly going to the shooting range with Thomas Cardingham, or training as a field agent, or containing the possible future path of a very senior ministry official who does terrible things for British "security". It's so easy to picture a more comfortable version of the book without Cardingham in it at all, where all the expats are sweet and tragic, or without that scary future version of Gore we never meet—but so much would be lost.
(And that's without getting into the backstory reason for Gore's initial interest in the bridge, which, like, talk about sinking dread. You know he feels some deep wish for redemption/atonement; you know his backstory, and when it all falls together it's like wow. yeah that makes sense. but holy fuck. Another excellent & horrifying choice for that to remain under the surface, unknown to the narrator.)
To me, these choices turn him from a lovely sketch of an attractive character (almost Wentworth-like?) into this uncomfortably real person. He's so out of his depth in modernity but he's a charming white British man, inured to violence, good at shooting things, and these qualities remain currency in our time. So no matter how much the bridge tortures herself trying to shape him, he can go where she can't, and is rewarded for it, and he slips out of her reach. Put another way: it ultimately is not in the interests of the British government to make an entirely modern man out of him, let alone a good man.
The political themes of the book depend on Gore's flaws, but imo so does the profundity of the romance. If he were perfect, if he didn't have these unsettling depths, loving him would be obvious, inevitable, and perfectly safe, the way love isn't in real life. Instead, it's something that torments the narrator, snags at her sense of self, and forces her to grapple with the fact that even someone you adore will contain awful potentialities, that they might become someone much worse because of something you said—and that the exact same relationship might make you both better, or it might make you both worse. Ultimately, the book lingers on hope, but it makes sure you know the stakes.