What tasks require or work best with a knife point? Most kitchen knives have pointed tips. I can imagine trying to improve safety (e.g. if they're accidentally dropped) by rounding the tip. For example, a paring knife might look like the one on the right instead of the one on the left:
 
But I wonder what is lost on the culinary side? I cannot think of a recipe where the tip is essential. Usually when I need a pointy thing a fork works better than the tip of a knife. Certainly there are knives with less pronounced tips such as the Santoku stye knife and carving knife.
 
The first has a less pronounced tip but could still cut through your shoe. The second had a rounded tip but is a more specialized kind of knife.
Imagine you don't have any knives with pointed tips. What tasks become more of a hassle to accomplish?
A pointy tip is useful in a boning knife, particularly when getting between meat and sinew, or getting under silver skin. The pointy end of the knife is helpful when removing meat from the bone. I also use the pointy end of a fillet knife to get between the skin and meat of fish, starting the separation, when I want to remove fish skin from the fillet. I use the pointy part of the knife to pierce pork skin, for example, when I want to string a piece of jowl or belly to dry.  I think you can accomplish plenty without the sharp point, but it does come in handy when you need to pierce or focus the cutting in a precise place. It's not really about recipes, rather it is a matter of the task that needs to be accomplished, and there are several where it comes in handy.