Still, as I recall, Socrates says he's interested in talking to him precisely because of his advanced age, and seems to hope it will be a more reflective time of life, when matters of the soul might loom larger than worldly affairs. And he crosses that interest with a question about his wealth, whether he can only spare his attention because of his financial security. (Maybe he doesn't specifically ask that, I don't remember, but he's interested in how much interest he has in money and why.) — Srap Tasmaner
I don't think we get an indication that Socrates hopes old age will be a more reflective time of life. The point is different. When Cephalus says that old age brings peace and freedom from the appetites, Socrates says
I imagine when you say that, Cephalus, the masses do not accept it. On the contrary, they think you bear old age more easily, not because of the way you live, but because you are wealthy. For the wealthy, they say, have many consolations. — 329e
And this is not just or primarily about how you live when you're old but about how you have lived throughout your life and what kind of character you have, a point that Cephalus has in fact already made. So Socrates approves of Cephalus to that extent.
Socrates next focuses on wealth and seems to drop his interest in old age. It's not clear how they relate to each other, but if old age is connected to power, as it was in prominent families of Athens, then the conversation leads quite naturally to Socrates' criticism of wealth and power in relation to the tyrants (Periander, or Perdiccas, and Xerxes, and Ismenias of Thebes). In other words, in the conversation with Cephalus it's not really about old age as such, but about traditional authority.
EDIT: I've realized that what I've said above is not a clear response to you. But I'll leave it and hope you can get something out of it.
To me, the idea of old age being naturally a philosophical period strikes me as quite reasonable and very Greek, if I may say so. At the other end, Socrates tries to get at the (noble) young before they're too caught up in responsibilities and cares. Also natural and reasonable, in the same way.
By "Greek" I mean that obsession with stages of growth and development, progression toward embodying your deepest nature, that stuff. — Srap Tasmaner
Good point. You can't be a philosopher king until you're 50. However, this is a final promotion following a life of preparation directed to the most noble way of serving the community, whereas Cephalus' turn to discussion in old age seems frivolous -- he has done the important work in his life already, and since he leaves the debate the moment he gets a difficult question, it looks like he's not so interested in discussion as he claims, or else he really just wants a chat.
But yes, Cephalus is not simply a bad or contemptible character. As is often the case in the Republic, Plato is dialectical in more than just the ancient Greek sense.