This is way off topic but it's the first time I've heard a parrelli person say that sometimes you need a more severe bitch...
Different bits have their time and place.
Coming from an English H/J point of view (seems like most posters on this thread are western), sometimes you need to bit up when jumping.
Doesn't matter how well trained your horse is, some of them get 'over stimulated' when jumping and need a tich stronger bit to get them back quickly.
For example, riding a strong jumper, you're coming in a bit over the pace to a triple. With a snaffle, you might have to sit way back and half halt HARD to get your horse back enough (and fast enough) that you don't both eat dirt. That big a move can seriously throw your balance off, as well as screw up your horse's balance and stride. If you have a stronger snaffle (twisted mouthpiece), or a curb (i.e. pelham, I hate kimberwickes), or a gag (depending on your horse) you can just half halt lightly, and make everything much smoother.
You also have to fight with them a lot less, which is better for everyone in the long run.
In the hunter ring, snaffles are usually preferred in a "ooh, look at how quiet my horse is!" kind of way. However, there are some 'interesting' mouthpieces that look like a simple snaffle from the outside (for example: Double Twisted Wire Full Cheek Snaffle Bit Horse Bit - Dover Saddlery.
Sometimes pelhams are used just to fine tune cues. Instead of having to move your hand, you'll simply have to close your fingers, and you'll get the same effect.
Pelhams are currently in vogue for eq for the exact same reason.
For dressage, I see no reason for using stronger bits. Not only are they illegal in the show ring, but there's usually no training advantage.
That being said, certain instances certain bits can be beneficial. In the right hands pelhams can help a horse who leans, or an elevator can help a horse who sucks behind the bit. But these are temporary schooling tools to fix specific problems.