Should we let kids fail?

There was an article over on the Guardian website about letting kids fail. I couldn't help myself. I had to comment.
I had to comment because people were burbling and buzzing along about "different these days" and "safety" and...well, you know what I mean.
I made a comment about the two boys around the corner. I have talked about them elsewhere. They are the two who have been brought up with what is best described as 50's style freedom. They  have survived and they are growing up into really good citizens. I like them. 
They tried all sorts of things and they failed - and they tried again.  The Whirlwind has tried things and failed - and tried again. (She has lost her temper with herself in much the same way as I did but she goes back to try again.)
My nephews and niece tried all sorts of things and failed - and tried again. 
One of my nephews and my niece have children of their own. My nephew's children are being brought up in today's more "protective" lifestyle. I suspect his wife was brought up rather like that. Their two children are constantly supervised. They seek adult attention and help. They already "know" that certain adult supervised activities are not negotiable and that their lives will be organised by adults.
My niece, my nephew's sister, has a quite different approach. Her children (younger) dress themselves without difficulty and the oldest (four) can tie her own shoelaces. They are expected to help around the house and they "help" to grow things in the garden - and they are expected to eat the broccoli and carrots and other things the garden produces.
They play, largely unsupervised, in the back garden. There has been a broken arm - falling off something - and a gashed head - running into something. They have been dealt with as "part of growing up".
And my niece worries about how she is going to continue to allow them to do all the things she believes they should be able to do. How long will it be before they are expected to go on "supervised play dates"? Already if a friend comes to play my niece knows that the expectation is the friend will be constantly watched.
"It's all about safety" and "You just can't let kids do the sort of thing we did" and "You can't let kids fail now. It's bad for their self-esteem."
I remember the Senior Cat failing a child one year. He did it after a lot of thought and discussion with the child's teacher and the child's parents. The child was very immature. He was, despite the best efforts of a good teacher, just not ready. 
The child was devastated. He wasn't going up with his friends. The following year he didn't even want to come to school so his teacher, the one who had tried to help, went to see him.
She told him, "You aren't going to fail if you try again. It's only people who don't try again who are failures."
He came back to school of course. He had to. His teacher kept reminding him quietly about succeeding if he tried again. 
I can remember this child because, as was the custom in the all age school, we older students had to hear the little ones read aloud from time to time. He would stand next to me and struggle with the squiggles on the page and then, one day, it seemed to make more sense because he read an entire page with almost no hesitation. He looked at me in a puzzled sort of way and then turned the page and went on to the next one.
At the end of it he burst into tears and told me, "I did it."
I hugged him - because you could do that sort of thing back then - and told him, "See, in the end you didn't fail." 
His teacher told him the same thing and gave him the "good reader" stamp on his hand.
He will have prize winning dairy cattle at this year's Royal Show but I wonder what would have happened if he hadn't been allowed to fail.