When you make a mistake often times you have immediate data, immediate feedback. Having spent 7 years as a pavement maintenance contractor, I have to admit that I made mistakes when striping parking lots and roads, but nothing as ironic or visible as this:
Sometimes our mistakes are very public. Sometimes we don't realize they are mistakes until some time later. But I bet the gentlemen (sorry guys, but I'm assuming a lady didn't make this one) who made this mistake will never misspell a certain word, ever again!
As an adult, the success of my professional life (and my parenting and husband-ing, for that matter) hinges on minimizing my mistakes. The way I do this is by using all of my knowledge and experience to make the best decision I can, in the most timely manner possible. Much of that knowledge and experience was gained by doing it the wrong way, many times. Hopefully I have remembered all of the wrong ways I did it in the past, or the wrong ways I've seen others do it to make sure this decision/action is better than before.
The phrase "Well, I'll never do that again!" is powerful. You did something wrong, and you learned something valuable from it.
Imagine how your child's world will be, how their learning and imagination and potential will flourish, when they know that they were free to make mistakes because they are a necessary part of learning! Imagine how much they will change the world because of the risks they are willing to take!
So, what's my point? Please let them fail. And when they do, teach them how to learn from it. And when they do it right or better the next time, praise their effort, their grit, and point out how it was because they learned from their mistake that they showed this growth. That is an amazing learning lesson they can use the rest of their lives.