I think you are somehow right while otherwise not. It is true that in the first two Craig-movies we see a fresh and new Bond, who is eager to get into the action and is maybe also driven by a bit of a juvenile arrogance (and passionate vengeance in Quantum of Solace). And yet in Skyfall we see a mature Bond who might still not be really grown up emotionally but who maybe has found the routine in his job (and is even a bit fed up with it), and we don't have to forget that it really is an exhausting job that might let you get old quite fast (and "00s have a very short life expectancy" anyway). And in the end he already had to make a carreer before becoming a 00, but I think it was rather the 90s when Silva worked for M in Hong Kong (though not with Bond, they didn't really know each other before). So much for the "physical" part of the question.
But while Skyfall indeed makes a statement about Bond (and the whole MI6 as an institution) getting old, it still makes clear at the end, that this is anything else than the end of his carreer and at the end he is indeed more ready to go on than ever before (maybe even strengthened by his experiences). This fits together with Skyfall's ambivalence of on the one hand continuing the modern rebooted line of the first two Craig-movies, while still going more into traditional Bond directions. It introduces classical characters, like Q and Moneypenny, while at the same time adapting them to the modernized line of the reboot.
In the same way MI6 is constantly depicted as (or accused of) getting old and useless now the cold war is over and Bond and M being relics of the past. But it is those old strengths that are needed to win against Silva who comes, like Bond, from the "shadows" of the past and is, with his madness, his desolate island he just "took over" and his whole attitude, more of a good old Bond-supervillain than anyone before him in the reboot. And indeed this is even emphasized by M in her speech before the court, when she says that "our enemies [...] do not exist on a map, they're not nations, they're individuals." And those individuals come from the good old times, like Silva and Bond. And this whole theme of reinvention of past virtues is both emphaszed by Bond travelling back to his own past in order to fight Silva on his own territory (and what could be older and more conservative than an old mansion in the Highlands) and this with the goold old DB5, an obvious nod to the old movies.
So at the bottom of the line you are right in that there is an obvious theme of aging of Bond (as a character but also his movie-franchise), while it is on the other hand emphasized that this old-fashionedness is what makes him different and thus a chance to use at his advantage and that both Bond and his movies should, while keeping at pace with modern developments, still not hesitate to remember their traditions. And what could emphasize this more than the overly nostalgic ending scene, which is both new in light of the reboot, but more old-fashioned than ever before when seen in light of the whole franchise.
As a last point you could compare this whole development to a classical midlife-crisis (whereas I'm not really in the position to have any personal experience with this). At a certain point you (and Bond) feel like getting old and don't know where to head on from now or if this might even be the end. But after this is over and you have accepted the "inevitablity of time" you try to make the best of it and start into a whole new and interresting part of life using your past experiences to your advantage. (Sorry if this last section is a bit too over the top in its stereotypicality ;))