The best I can do, after raising two children, is that fatherhood needs to be less about keeping your children alive (by avoiding risk in any form) and more about teaching them to 1) survive on their own in the world, and once they're in a good place, 2) incrementally building the life they desire. In the most general sense, that means: How to size up a situation, analyze it for both opportunities and risk, asses the resources available and then resolve it. You can't really teach your kids to size up situations without, at some point, exposing them to said situations. Moreover, there is much more of an edge to that process when a child knows they are on their own in solving the problem.
So it's a real balancing act as a father to present age & maturity-appropriate situations that challenge your child without presenting more danger than they can reasonably handle. Anxiety, yes, that's the fuel to keep fathers focused on maintaining that balance. Dread? Yes, but you'll get over it once your kids start surprising you with insights and behaviors you didn't know you'd taught them.