It's not clear to me how you build grit and resilience in kids.
Not clear here, either. But, I do know that the helicopter model is certainly not the way. I think you have to let them fail. Certainly, you do not let them fail at the really dangerous things--but, they need to know that they are not going to always be the "best". And, somehow, they need to learn to be happy to observe the success of others.
You need to allow them to be sad at their disappointments--if they do not get the toy they want right now. How many of us have been out the day after Thanksgiving trying to secure the "hot" toy for Christmas? Nothing wrong with that. Occasionally--but not always. When you have dinner and they don't get what they want--don't go and fix them their own dinner. I have a friend whose child would come home from daycare (home daycare) and be obsessed with the toy the other child received. Mom would go right out and buy the same toy for her child.
Let the three year old throw the tantrum--rather than "negotiate" and give him whatever he thinks he wants.
If your child does not get on the team he wants--don't go calling the coach and weaseling your kid on the team. (This happens. I know people who have done this.) Let him be disappointed. Be sympathetic, but help him see that we are all disappointed, but there will be other opportunities.
I read somewhere that you learn more from your failures than your successes. I think that might be true.