I'll try to explain some stuff. First things first, most people, until you get to an advanced level, drop their hands by accident or lack of training. I'll get to that later. As for Silva, he throws in an agressive straight foward way, people are afraid of his strikes so nobody counters, and you'll notice everyone that tries to counter knocks him down (Ortiz, Sakuraba, SHUNGO OYAMA). That's for Silva, as for dropping your hands, I'll spread it around 3 parts.
Boxing: There is a difference between dropping your hands in boxing and lowering your lead and bracing with your shoulder. One of the biggest things is that people dont usually see a jab coming from the hip area, and it is hard to react to, meaning the followup is easier. You can parry a right hand with your left shoulder and counter with a right hand of your own. You can see better, so you can react quicker, and as long as your lead shoulder is against your chin it will be difficult to be knocked out. It helps your muscles stay relaxed, I find it very useful at times. And, it's unorthadox, it throws peoples games off. One thing you need when you drop your lead hand is head movement, make sure you have head movement. When people throw a bunch of punches at an opponent that is dazed in a corner to try and knock him down/out, there is very little chance of the other person firing back, so the attacker just unloads for power. If the guy does try and counter, the boxer has head movement and can avoid that one shot, and continue his barrage. If the person recovers, and the other person is still unloading, he is asking to be knocked out with his hand the way they are.
Kickboxing: Laziness, to just relax their arms, and they think they are boxers. (I kickbox, so no biased opinion)
MMA: Stop the shot, and since most guys arent A level strikers, it throws them off much more. And they think they are boxers.
Hope this helps.