A rider curses because her horse refuses to be bridled. He shouldn't make such a fuss, she thinks. The mouthpiece is no bar after all (and therefore not severe). Well. The mouthpiece might be a snaffle but there is more to it: two shanks, to be precise. This combination (a snaffle mouthpiece with leverage) is available in different designs and features - here in Europe it's usually called a Pelham. 

What kind of shocks me is the ignorance concerning its mode of action. This bit combines two functions (snaffle and lever) without the rider being able to apply them separately. This is why this bit sucks for horses. 

A classic snaffle bit. Design: Nadja
Let's have a look the good old snaffle bit. Two pieces of metal, linked in the middle, the left rein talks to the left piece, the right rein to the right piece (a snaffle consisting of three pieces waters up the separation of left and right). This bit is ideal for lateral work - asking for flexion in the neck or giving at the poll lateraly. In general it talks to one side of the horse more than the other. 

Now let's look at the leverage bit like a curb. The mouthpiece is a bar. It's not built to adress one side of the horse's mouth or jaw. If you pick up the reins (which ideally are operated with one hand), the bar rotates in the mouth, the chain around the chin tightens as does the head stall which increases pressure at the horse's neck. This pressure is not lateral, it applies to both sides. The curb is made to tell the horse how to carry his head and neck - give at the poll, bridle up or lower the head in a forward down position. 

The curb is made for vertical aids, the snaffle for lateral aids. As a rider I want to separate that out strictly. And that is exactly what is lost when using a combination bit. When I pick up the reins, I not only adress the snaffle in the horse's mouth but also the lever. Both have completely different meaning to the horse - and my undifferentiated rein aid mixes both up

In my opinion it's impossible to give a clear aid with that kind of a bit. This is why no serious horseman uses or recommends it. 

If you look at dressage, the curb is always combined with a snaffle. The horse then carries two mouthpieces at the same time, and the reins control the bits separately (though some ways of holding the reins make that hard). 
The baroque rider who guides his horse with only a curb uses his seat to give lateral aids (as in flexion of the horse's body or position of the neck). They don't need an additional snaffle. Neither do the Californian Vaqueros - at least if I understood Jeff Sanders. It would make sense: The bosal (the hackamore) traditionally is an important part of the horse's education. And it is not a tool that is ideal for lateral aids. So these cues need to come from the rider's seat and legs as well. 

A Tomb Thomb Bit: The mouthpiece looks
like a snaffle but it features shanks.
Design: Nadja
The combination bit is usually referred to as Tom Thumb Bit. Mark Rashid wrote a clear analysis why it makes no sense (to the horse). Rick Gore's point is the same - he conveys it less profoundly, but very plainly in his choice of words.

PS: My personal favorite display of complete ignorance is a comment under the mechanical hackamore from a German online horse outfitter. It says: "Ideal for hot horses, as the cheap hackamores usually break under the strain". It doesn't get any worse than this. 

PPS: Another sign of little savvy is using a leverage bit on a horse, combining it with a martingal and justifing it with the horse being a chronic rearer. You don't even have to understand the mechanics behind the bit to understand how stupid that is. Just have a look at the words, with the leverage bit also called elevation bit and the martingal also called a tiedown. So using both at the same time the rider basically says the horse: "elevate the neck and lower the head". What would I want to communicate by that apart from the fact that I am absolutely clueless?