Actually I had made all three points already. 
But AskNott gave a good historical explanation on how and why the knee dragging technique started. Note that racers were already leaning their body towards the apex of a corner before that.
Couple other things:
It is normal to accelerater through a turn, so moving the CG of the rider/bike system toward the inside of the turn causes a turning moment (due to imbalanced inertial forces) as the bike acccelerates.
In order to avoid instability (AKA “tank slappers” ) racing motorcycle steering geometry is somewhat compromised in that steering forces may be on the high side. This is exacerbated by the need for narrow handlebars (“clip ons”) which offer good aerdynamics, but poor leverage. By “hanging” off, the neutral point of the steering is shifted such that steering forces to maintain the turn are are reduced. This allows the rider slightly improved “feel” and also can help minimize the upset if/when the tire starts to slide.
A “chicane” is at least two turns with essentially no straight between them. If the rider can flick the bike from one turn to the next quickly enough to keep the suspension from unloading much, then he can get through the turn quicker. Moving around on the bike and hanging off can speed the transition from turning one direction to the other.
Lastly, of the ways to crash, going over the top of the bike, toward the outside of the turn (“highsiding”) is among the worst. Hanging off toward the inside makes it slightly more likely that the rider will experience a slightly less traumatic “lowside” get-off if the traction goes in the toilet. Imagine that the bike itself highsides. If the rider is hanging off the inside, then only the outside leg is “pushed” by the bike. If he were hanging off to the outside then the seat would be pushing over the top by his CG. The difference is between a sliding smoothly to a stop wreck, and a catipaulted through the air into the fence wreck.
Upon re-reading, indeed you have Pedro. Apologies for the duplication, and consider your points validated!
As well as the extra turning moment from accelerating through a corner that Kevbo mentions, an advanced racer will deliberately set up a bit of oversteer to point them in the right direction. That takes some nerves of steel to do that on two wheels.
High-sided accidents are nasty enough on a bicycle. On a motorcycle they’re lethal. Imagine a sizable chunk of your forward energy being translated into slamming you into the ground square-on.
Low-sided accidents are a doddle. You just fall on your arse and slide along for a bit.
The other fun part about a highside is while you are flopping down the track like a limp rag doll, the bike is cartwheeling along and might smash on top of you.
Another friend of mine did this at Lime Rock. The bruises all over his torso from the bike landing on him were horrific.
I was living in California during that time period when they decided that a special written test should be required for a motorcycle license (fortunately, I was ‘grandfathered’). A friend of mine was complaining about some of the questions on the test. The only one I can remember right now is “T/F: A good way to go around a corner is to put your inside foot down.” They gave the answer as T! :smack: After listening to some of the other questions, it became obvious to me how they had made up the questions. They had sent someone to the races and watched what the racers did, ignoring the fact that the racers were in a competition, wore full leathers with padding, wore heavy leather boots with steel sole plates, and the like. 
(After I figured this out, I could answer any of the questions “correctly”).
All the talk about leaning the bike reminds me of a couple of amusing incidents involving experienced riders and bikes with sidecars. My cousin, a big strong guy, and his tiny wife brought home a Harley with a sidecar, with his wife in the sidecar. Every time he would take a turn with the sidecar on the outside of the curve, he would lean the bike and lift the sidecar completely off the ground. :eek:
The other guy was a friend who was trying out a bike with a sidecar out in an open field with a single tree about 200 yds. away. He said he almost ran into that tree before he finally realized that he needed to turn the handlebars and not lean the bike. 
Brady