Shadow Priests are not really in demand especially for the harder content.
In heroics, the SP doesn't really have time to get their dots ticking before the trash (or even bosses) are dead. Even using the AOE spell (mind sear) it is still hard to do particularly high dps as the mind sear target doesn't take damage.
In 'easy' raids, such as Ulduar and normal TOC, the Shadow priest does reasonable dps and you should expect to do a fair contribution, although it is here that you will see that the SPs are currently underpowered and a decent SP wearing epic items may see themselves being overtaken by some classes wearing significantly worse gear in DPS.
When you get to the harder content (TOGC), then SPs really struggle. You are likely to be near the bottom of the DPS meters and many top guilds have left out shadow priests for this as they don't do enough dps.
The SP utility is lacking now as well compared to other hybrid classes.
In the next patch there are going to be buffs to SP damage..some of the dots are going to be affected by haste and so I expect SPs may be a bit better. Not sure how much though as i've not had time to look into it.
You clearly have never played with a decent SP. We raid with 2 sp's and they both pull 6k+ they are always in the top 10 on dps. and easy keeping up with our dks and palla on dps on anub25 hm.
SP DPS is very very good - if played properly. They are as good as a mage/lock/boomkin if played properly.
They are slow until you get shadowform.
Best bet is get a recruit a friend. Level with ur mate -mages are nice, and just he AoEs and you heal him. We did this with mage, priest and lock.
Leveling is really quick and easy now.