The timelessness of the character is arguable. James Bond can also be seen as a personification of anachronistic imperialism and jingoism, as well as "a sexist, misogynist dinosaur, a relic of the Cold War."
And I say this as a long-time Bond fan.
Kor
The idea of Bond being a man out of time has been there from the very text that Fleming wrote. He's the last man standing for the British Empire of olde, in a world where the US and the Soviets became the dominant superpowers. In CASINO ROYALE it's very intentional that on the card table you have Le Chiffre representing Soviet Russia, Felix Leiter representing the USA, and Bond for England. What happens when Le Chiffre cleans him out of the game? Felix comes to the rescue and bails out Bond by lending him money. WW2 replayed on the casino table. It's even more blatant in the novel YOU ONLY LIVE TWICE, where Bond is having multiple geopolitical discussions with Tiger Tanaka, and how England and Japan is trying to catch up with the ever changing dynamics of the world. So by keeping Bond white, the films can actually maintain that subtext.
Speaking of the NEW film, it's actually interesting that the movie has Bond at the beginning of the film residing in Jamaica, a country that declared its independence from the Empire nearly 60 years ago. It's as if he's a ghost of the British Empire that hasn't learned to move on with the ever changing world.
Of course, the aspect of Bond being a man out of time wasn't really a thing in the movies until arguably the 70s, when Roger Moore had to team up with a female agent that represented modern Feminism. Then by the 90s that changed to the new world order with M calling Bond "a relic of the Cold War" in the film GOLDENEYE. Then in SKYFALL Silva mocks Bond by bringing up "the Empire" as a dead relic much like Bond.