I don't know about pain, but for anxiety there are other drugs that are intended for long term use. The ones I'm aware of (mirtazapine and venlafaxine) are also used as anti-depressants.
Benzos generally treat acute anxiety where serotonin/norepinephrine reuptake inhibitors treat chronic anxiety. Further, some folks don't tolerate SS(N)RI's very well, they have wide-ranging and difficult side-effects.
Yeah, I can see where there'd be cases where SSRIs and SNRIs wouldn't work out; everyone's situation is a little different.
It seems like there's a problem in the general case though, if you have doctors that are a little too quick to prescribe benzos and refer the prescribing of antidepressants to a specialist. For those that live in an area with a shortage of mental health professionals, it might take a month or two to see a psychiatrist (and then maybe only after talking to a therapist or something first), and then maybe a few weeks more before the antidepressants start working, which is longer than anyone ought to be on benzos if they can at all help it.