What does mast rake do?

It's not obvious why increasing rake would open the slot, or why that would result in depowering. If your boat allows it, try sailing with a very closed slot. More power? I suspect not.

And allowing the centreboard to be lifted, fine except that I can think of classes that, as the breeze builds, will start to rake the rig long before they'd consider raising the board.

I'm not disputing that rake works but the explanations you commonly read don't really bear examination.

Increasing mast rake opens the slot on most boats as the head of the jib moves aft relative to the rest of the sail. This opens the leech of the jib so the slot has now been opened.

No kicker in dinghys can work. Has to be really windy, and then allows power on/power off to only be a small amount of mainsheet.

Garry,

A basic understanding of vectors demonstrate that the faster you go the higher you point.  so why should easing the sheet a little stop me pointing, except in the short term whilst I accelerate?

The practice of increasing mast rake in more wind is about giving the wind a different aerofoil from that used at lower wind speeds.

Rake should not be confused with bend. 

Bladed sails, caused typically by lots of cunningham and less kicker when windy are fast around the course.  This may actually be due to making a lightweight boat easier to sail as the top of the sail is controlled better rather than actually increasing straight line speed, but they are fast around the course .

Maintain some curvature in the sails in the light stuff, don't have bags in the sails but at the same time, don't have them flat. There are two schools of thought with light wind settings, but flat sails to reduce drag theory also kills all lift too and is very slow. Maintaining some curvature maintains a profile optimum for generating lift. High Performance Sailing by Bethwaite and Sail Performance by C A Marchaj, both cover the theory in great depth, Sail Performance is more specific. Best to read a book about it instead of trying to understand bits and pieces from a forum if you are really interested. We don't adjust mast rake on the 49er as we have a fixed forestay but in the light stuff we don't bend the mast extensively to move the centre of effort aft as is the effect with raking as it is a depowering method, probably why Alex was saying keep the mast straight initially. If you bear in mind what Ian was saying about wings on the 747 and Concorde, it's a good analogy of sail shape. The 747 wing shape with more curvature is designed that way to generate maximum lift to carry a high payload whereas concorde's wings are very flat with the aim to minimalise drag. The 747 shape will help on light days to maximise lift at lower speed and on the windier days when you have plenty of lift the aim is to flatten sails off to reduce drag.