Talking about Clara Oswin Oswald is near impossible without employing spoiler cuts, which may be part of the problem - or the advantage, depending on your point of view. Recently, I stumbled across a clever observation of elisi
's, to the effect that back in 2005, when RTD had to relaunch and reintroduce Doctor Who
to a new audience, the Doctor was (to many) the unknown, the mystery, whereas the Companion, while also a new character, was the familiar (living in easily recognizable and identifiable circumstances). By the time Moffat took over as showrunner, the Doctor was more than familiar to the audience; and thus, Moffat made the Companions the mystery. Or rather, mysteries.
This of course is one of the chief issues of the yay and nay sayers of the entire Moffat era. Personally, I think it sometimes works and sometimes doesn't. It mostly works with Amy in her first season; I still have a problem with the way the whole crack mystery is handled (i.e. ultra important when it's an arc episode, not a problem when we get a standalone), but Amy herself, personality-wise, comes across clearly from the moment little Amelia Pond prays to Santa. (I didn't "get" Amy emotionally until about mid season, but that wasn't for lack of a sense of personality; retrospectively, I wondered whether it might have been, but now the international iPlayer has put up the fifth New Who season online, and rewatching early Amy episodes confirms she's there from the start.) The mystery as to what the crack in time has to do with Amy is solved by the end of her first season, but that's not the key to her personality, and Amy remains interesting beyond its solving.
"Who is River Song?" is a mystery set up already in the RTD era via the Moff's Library
episodes and key to the first two Moffat seasons; while I have considerable problems with the ultimate answer, River in season 5 is an incredibly compelling, interesting character, and her appearances are not dependent on providing an answer to the question for their appeal. It was, perhaps, only to be expected that when Moffat introduced his next regular Companion, she, too, would be a mystery, and she, too, would meet the Doctor out of sequence; Moffat really does love the timey-wimey, and he is, love him or resent him for it, undoubtedly the DW writer who does the most with the possibilities and paradoxes of time travel.
The problem, to me, with how the Companion-as-mystery gambit was executed the third time around isn't that the introduction wasn't good, or the question not interesting. It's that the introduction(s) was/were maybe too good, and the follow-up paled because the very set up of the question made it impossible not to. ( And now I really must employ the spoiler cut )