I've got just about every hawkbill Spyderco makes. (Only missing a harpy and the discontinued superhawk).
Seems like you've got a grasp of the general function. Material won't slide off the edge like with a traditional knife. That can be advantageous in some tasks. In particular when you need to cut away from something as opposed to into something. Especially if you need to get under or behind something and pull it towards you. Like cutting a rope, or a strap, a seatbelt, even clothing in a rescue situation. The curve allows you to get under and behind what you need to cut, and allows you to make the cut towards you and away from the thing you dont want to damage. Pull cutting lets you put more force into the cuts as well.
In IT I often had to cut zip ties off bundled cables. This wasn't possible with a regular knife without accidentally damaging the cables. I'd use the tip of my Hawkbill Dragonfly or ladybug to hook under the zip tie. The flat spine of the knife was against the cables so no danger of cutting them, then I'd pull cut it towards me and away from the cable (it takes a bit of force to pop off a zip tie even with a sharp knife).
I also had to regularly open boxes that had things like monitors and other things you didn't want to damage inside. In much the same way as I cut the zip ties, I could use the tip of the hawkbill to to make a shallow cut into the box or package keeping the spine facing the inside, then basically cutting up from the inside of the box outward.
Another use you may not think of is using the tip to reach things on high shelves, like a role of paper towels thats just out of reach. Did that this morning with my Matriarch
Besides the regular hawkbills I've also used the Karahawk Karambit as a Utility knife with great results, it was designed for defense, but the wave opener, retention ring, and powerful leverage make it a superior Utility knife.
I'm also far from the first person to do so, here's a great old thread about using the Karahawk as a warehouse knife.