Don, for an Epicurean god, perhaps, but for a human being?
I can see why you would be tempted to take that position due to the passages which focus on how particular fears can be reduced or eliminated through particular means, but I see "anxiety" as a subset of the overall pleasure-pain doctrine and not as something unique in itself.
And in fact I would see the temptation to consider it to be unique is one of the most dangerous aspects of the way some people elevate tranquility to be the goal rather than pleasure.
It seems to me that this is one of the ways in which we should see Epicurus as building on the Cyreniacs rather than refuting them. If the Cyeniacs really wanted to deprecate the wide variety of mental pleasures that exist, then they were wrong, but I have a very difficult time thinking that they were so narrow in focus. Epicurus, as Diogenes Laertius says, recognized *both* active and non-active pleasures, and in so doing he tightened up the logic of the prior advocates of pleasure and made the theory stronger as against the Platonists and the others who advocated other versions of "the good." If the good is pleasure, then that includes all kinds, and Nature doesn't tell us "pursue pleasure, but of all the pleasures, pursue tranquility the most" -- At least I don't personally understand Nature as doing so, nor do I observe that in the young of all species, which I gather is the ultimate observational test.