Why is it that so few schools teach children how to speak in public?
It is not difficult, all you need is a debating society.
I am fortunate enough to have gone to a school where the debating society was the thing to do. Even on a cold winter with snow outside two hundred or so of the thousand at the school would show up, of their own accord and without anyone telling they had to go. To be voted by your peers onto the committee for the debating society was the ultimate in status. Our debating society made public speaking a fun thing to do.
As well as being able to propose/oppose a motion from the stage with a self-prepared speech it was also possible to learn how to listen, ask questions from the floor and respond to points made.
So, when I left school, I had a head start. I had spoken in front of a crowd on two hundred or so occasions from a very safe sandbox. In my adult life this experience has been invaluable. I know about what happens if one is not totally prepared. I know what happens if one is over prepared - i.e. reading instead of talking. I know about posture and how to make meaningful eye contact with a sea of faces. However, most importantly, I knew that public speaking was a desirable thing to do, a privilege.
If anyone reading this has kids and their kids are not involved in a school debating society, think about it. Get together with the school and a few teachers and sell them the idea of a debating society. Get someone charismatic - a head teacher who has to present in front of all the kids - to make the debating society the most important thing he/she does. Your local posh school will have a debating society, visit them, learn how they do it and steal their procedures and organisational structure.
Then, if you are lucky and the school debating society kicks off and becomes the thing to do, your child should grow up to be a darned good public speaker. What they will learn from that will help them no end. If they also end up knowing a subject inside and out at some stage of their adult life they should be able to literally wing it without having to use any of the silly suggestions presented on this thread (betablockers - you must be kidding!!!).