Based on Xtian's comment on my post from earlier, I took the Shadow Priest for another spin, this time making sure to focus on nuking instead of DOT's. This proved far more effective. I'm still less than fond of having a channeled spell as my bread and butter DPS, but at least I don't feel like I'm doing it wrong anymore. Apparently that tasty passive mana and HP regen that my mage enjoys when a Shadow Priest joins the group is one of those perks that one saves for when one has a tank.
Meanwhile, What's My Main Again? suggested that I try the talent that lengthens the stun duration on the cat's stealth opener by a second. A single second is one of those things that sounds stupid in the abstract, but in this case makes the difference between having the enemy come un-stunned before or after you've shredded its rear to mangled bits.
I still think that I'm more interested in OOMkin than the cat side of Druidism - a good thing since the combination I'm describing isn't even available until level 50 (!) - but adding the stun talent might elevate the spec from "don't bother" to "worth keeping on a dual spec slot".
Druids are the only class that has separate resource bars - a Shaman can dual spec caster DPS and melee DPS, but both sides use the same mana pool, which will be emptied when you click the switch spec button. By contrast, a Moonkin who runs totally out of mana 7 kills into a kill 10 rats quest can shift to kitty form, switch to a feral spec (you shift before respeccing because shifting costs mana, which you would have to regen after you specced), wait 5 seconds for their energy to regenerate, and go. Throw in the utility of being able to go into stealth mode, and this could be well worth the cost of dual speccing at level 40, even on a character that I'm not intending to use for group content.
Meanwhile jumping, clicking storm crow form, and instantly flying off is a very neat trick. So is dying your hair and having your cat form change colors. I can imagine clicking the barber button very frequently on the hypothetical Worgen druid if this is the type of perk I can look forward to. :)
Oh hai, I changed colors.