Are characters who are beautiful women not allowed to be wrong, then? Although it would be useful to explore how much and in what ways she's wrong, which we won't get to do with the Ponds now.
Stepping outside the shows internal universe, there is clearly a problem in that most female major roles (in general) go to young attractive women and most companions only stick around for a couple of years, so in practice the Doctor has a constant stream of young and attractive females who never age particularly and that's not necessarily sending a good message even if the message is accidental.
In fact River has been a welcome exception in that, while beautiful, she's older than the standard companion and she's stuck around. But I agree with you insofar as that that makes it infuriating that she's the character chosen to be insecure about ageing (although it's not entirely out of character, as she never originally expected to have to age and die). Also, of course, they've written themselves into a corner and she can't stick around indefinitely getting older and older to offset her current insecurity.
I suppose essentially yes, I agree it was unnecessary and could/should have been better written. But I disagree that Eleven's being written as a superficial youth-obsessed git, because his actions and words don't match what River says. On a hypothetical third hand, River is being written as more insecure than necessary.