Thanks for your thoughts! Anyway, I also have a Latias on my team, a Togekiss, and an Electivire, so that covers the Psychic thing. Also, all of you are forgeting one important factor, explosion isn't the only move they know.
Even so, having three Pokemon with Explosion seems a bit overkill, especially when you made it sound like that was their big purpose.
For example, if I have out Azelf and the opponent has out, I don't know, mabye Gengar, I use U-turn to Togekiss, take the impending immunty hit, and hit with a Choice Specs Air Slash, or have Snorlax use Choice Band Crunch and then switch next turn.
I never said I thought you would be stupid enough to use Explosion when a Ghost-type is already out. I'm saying that they can easily switch a Ghost-type in during the turn you use it. Azelf, Metagross, and Snorlax all commonly run Explosion/Selfdestruct (Snorlax is a bit less common, but Ghost-types still like to switch in on non-Crunch variants to eat its STAB Return or Body Slam), so opponents will expect it and act accordingly (maybe it's a little less expected in Azelf, since no one expects a physical set, let alone a Choice Band). It's not like Ghost-types are rare, either. Gengar, Dusknoir, Froslass, Mismagius, and Rotom-A (if you're using Shoddy) are all fairly common from what I've seen.
Also, sreservoir, Lickilicky will reach 250 if I'm lucky in attack, while Snorlax will easily reach 300. I also feel that Snorlax's extra 50 base HP will allow it to survive almost anything with some EV's in defense.
Adamant Lickilicky hits over 400 Attack with a Choice Band - hell, so can Jolly if it has good enough IVs - and is the only thing in the game with STAB Explosion. 375 base power coming off 400 Attack while ignoring half your opponent's defense is going to seriously mess things up. Also, he never said specifically get rid of Snorlax, just consider Lickilicky.
To be honest, I most likly won't use Explosion on Metagross, It's just a last resort against things with high enough attack to prevent more then one move.
That should be Explosion's purpose - a last-ditch effort when you're about to die. You shouldn't have to use it more than once, twice in bad situations. Don't expect to fall into the situation you described too often, as Metagross and Snorlax are both very slow.
The big problem you have here is that Choice Band forces your Pokemon to be a suicide bomber. You can't switch to Explosion when you're about to die, so the last-ditch scenario Explosion is most commonly used in can't happen; you have to switch out to something else. The only time you'd find it practical to use it is when you get smashed while switching in to use something else on the opponent, and then you have to somehow find a way for Metagross or Snorlax to outspeed whatever hit them hard enough to bring them into the danger zone. Sure, you can get a kill on the switch if your opponent doesn't predict correctly, but it's usually a much better idea to predict their switch-in - that way, you still kill the opponent, and you're still alive.
Snorlax doesn't have a prayer of ever outspeeding anything, so it can only use Selfdestruct if it avoids being 2HKOed or if the opponent switches out, which will most often be to a Ghost-type as they expect a STAB Normal attack. That leaves Metagross and Azelf; Metagross has only 70 base speed and therefore still can't outspeed a lot. I know you said you probably won't use Explosion a lot on him (or at all, you weren't clear on that), but when you outright say you'll rarely use it, it's time to reconsider it as a move choice. Explosion is still viable on Metagross, but not to the extent you seem to think it is. And finally, we have Azelf, who, while being able to viably use Explosion on a Choice Band set, is a powerful sweeper in its own right, and almost seems to go to waste when it simply explodes at the slightest threat. I'd go with a Naive Azelf set focused on special attacks (without any Choice items), and put in just enough Attack EVs to get some vital OHKOs with Explosion - that way, you have a more versatile attacker. However, ultimately, a Choice Band set could work for its pure unpredictability. Imagine watching as your opponent switches in a Blissey and ends up eating a STAB Zen Headbutt (I'm pretty sure that would be a kill, but I'm too lazy to pull up a calculator right now).
Bottom line: Your team could work, but it's a bit risky to put so much focus on exploding.