Un, no. You must not have much knoweldge about other classes. Shadow Priests are worst class in the game for belts and are the worst caster in the game when it comes to mobility on fights.
If you ask a shadow priest to go on belt they always have to save DP3, which means their dps priority through out the fight becomes significant hampered. They Could Save Mind Spike charges.. DP3.. but this is really suboptimal. Where as you could just ask a warlock to go on the belt and cast while moving.
-Have no teleport ability.
-They cannot cast while moving(unless they have procs available) - Warlocks can with Kiljadean Cunning talent.
-They cannot channel mind flay while moving(significant for things like DP3)
Elemental shamans and Warlocks are the best caster to put on the belt and in general elemental shaman, hunter, warlock, are top choices for belt teams for ranged options. Priest/mage should be last option for belt in almost any group that wants to optimize performance of the entire raid.
Now if a SP/Mage wants to hop on the belt because its fun and they're good at it and it doesnt hamper raid performance then good for them. But in general its just not an optimal strategy.
Pretty sure I know other classes but it would seem that you don't know about Levitate. I guess you're not ultra knowledgeable about other classes or at least as much as you'd like to think you know.
If you absolutely had to choose, SP are the best caster to put up there since they have the ABILITY to save a large DPS "cooldown" (DP>MF:Insanity) for every belt they go on. Warlocks, Mages and Ele Shaman will be of MUCH better use on the mines spawning than a SP casting Mind Sear hoping it hits the adds.
From our experiences and mine playing my warlock, you're much better suited to be on mines or on the boss. Yes you can cast filler while moving, but getting good chaos bolts off on heroic is a lot different then simply lining your back up against an open space that never changes on normal/flex. The lava beams on heroic move and the gaps are constantly changing, while warlocks can spam filler fairly easily, it's not all that much damage.
Priests are actually really good on the belt for a lot of reasons. First levitate makes the belt a joke once you're up on it, and they can always bank orbs for an instant 3 orb devouring plague when going up.
Generally hunters, priests and pretty much all melee are desirable on the belts. Most of the reasoning is they are completely mobile (priests with levitate) and don't really get hurt by movement. Warlocks don't get hurt by movement that much either, but it's still a pain in the ass on HEROIC to get good chaos bolts off if you're planning on doing the belt.
Furthermore aside from hunters, the rest of the caster DPS are far better suited to doing mines. And actually surviving on the main platform. It's not so much a function of warlocks being miserable on the belts, it's allocating other DPS to their strengths/weaknesses. Priest AoE isn't exactly stellar.
As main hunter who goes every single belt in 25hc and who plays as alt main warlock, it your raid leader is telling you to go belt in hc just tell him to suck it up and put any other class there. Warlock is way too good class to put in belt. In normal warlock is good to go on belt since you see open spots, in hc even smallest false of positioning causes your dps to go through the FLOOR. And this is for destro, affli and demo are worse than disc priest in belt.