This is actually a bit of a complex issue.
While SSRIs have a lower efficacy than benzodiazepines (they work less often), their efficacy is still substantial, around 60-70% of people with anxiety disorders respond well to an SSRI, with the similar ability to swap between them for second tries (tiny differences between them mean one may work when another doesn't). Secondly, when they do work, they work (again, in general) about as well as benzos. They also, in a sense, have less problematic side effects: certain side effects of benzos can cause quite a bit of impairment, while the two big ones from SSRIs r less immediately concerning.
However, there is a middling bit of evidence that suggests that the antidepressant success rate falls off pretty sharply when u get into the more 'severe' end of anxiety disorders. The ones that r really disabling, disruptive & intractable.
Secondly. What you're describing is not addiction. It is physical tolerance. Check out http://painmed.org/pdf/definition.pdf for an explanation of what addiction, tolerance & dependence actually mean, especially in a medical context. Not the socially contrived paranoia. Addiction means impaired control over drug use, & consequences from that use & continued use despite serious harm. We see this occasionally with benzos, but -never- with SSRI antidepressants. This leads me to my second issue.
There is a pervasive stigma attached to benzodiazepine tranquilizers that is quite severe & dates back approximately to the early 1970s. At the time, with the war on drugs going heavy, it came to light that heroin addicts - society is ultimate problem - would, given no alternative, consume large quantities of benzos. This triggered a bit of a moral panic, as Valium & its relatives were one of the most widely used prescription drugs in America. Traditionally one of the populations with the highest prescription rate for such drugs has been middle class married women. A fair bit of sensationalist media painted the drugs in such a negative light & provoked a rather severe moral panic & backlash against the drugs. This was further amplified by some bad decisions in the formulation of temazepam (restoril) which was manufactured as a liquid capsule with the liquid inside suitable for injection. Of course, the only people who would do that were junkies, but the formulation made it incredibly easy to do.
This stigma is so long lived, so pervasive & strong, that it has penetrated the medical community. However, this stigma is completely false - completely contradictory to the clinical data. There r about four million Americans who have used benzodiazepines from a period of five years to multiple decades. Without tolerance (tolerance to the anxiolytic effects is a biochemical impossibility), without abuse or addiction, & without increasing their dose. This pattern is mirrored in developed countries around the world. And we know the risk factors for benzo addiction - basically people who r addicts, abusers of another substance prior to benzos.
And yes, actually most doctors would probably try Paxil, or Celexa/Lexapro for their anxiety first. The citaloprams r gaining popularity because they anecdotally work better, & have less obnoxious problems than paxil.