We almost never pick up our son when he falls and never really have once he could stand up on his own, even when he was first learning to walk. We calmly go over to him, check in to see if he thinks he's ok and tell him we're there if he needs help. We always let him get up on his own if he doesn't need or want help, he checks in on his own injuries and self assesses but we are always right there if he needs or wants it. It is incredibly important that kids learn to self assess IMO.
When he was very little (1-2ish) I used to get daggers from parents at the playground all the time when I wouldn't run over to pick him up or fawn all over him after he bailed. I'd be crouched next to him with my hand out telling him I was there if he needed me, checking in on him, but very specifically not picking him up after a bail and people used to hate it. This was all done in a very loving, teaching, supporting manner so that he could learn to trust his own judgement and learn independence and never even remotely a "toughening him up" kind of way. One day he tripped while running max speed and fell pretty hard for a toddler and just got up, looked at his hands and knees, and then just took off playing again. There was a man and 2 of his grand kids at least a couple years older than my boy playing nearby, the G-pa just said to me "If that fall happened to one of these boys our park trip would be over" and I was so proud that our little guy was able to check himself out and realize he was fine and then just keep going all on his own. We gave him the tools to make sure he was or wasn't OK and the confidence to ask for help.
He never ever freaked out about getting hurt because we never freaked out about it.
Edit - I'll add a few more of my thoughts on parenting as a whole I guess cuz why not. We almost never outright warn him about minor danger, ie; playground falls, kinda steep hills on his bike, balancing on stuff, generally things that won't cause actual bodily harm if they go poorly. We don't really say "Be careful" or "That's dangerous," because I think those are kind of empty statements from a learning point of view. While those might be valid things to say to an adult who knows how to make decisions the statement doesn't really help a kid learn how to make those decisions themselves or how to recognize dangerous situations really.
What we do do is ask him questions like "What kinds of things do you think might happen if this doesn't go the way you're thinking it will?" or how he could best prepare himself if he's trying something new. If we do have actual input it will be along the lines of "Those rocks look pretty wobbly, do you think there is a different path you could take or a different way to get around / over / whatever?" We try to ensure the decisions are his own to make while simultaneously highlighting the things that could trip him up. Teaching the thought process that goes in to making a decision is much better for him than just telling him not to do something.